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Modeling the effects of hydrodynamics, suspended sediments, and water quality on light attenuation in Indian River Lagoon, Florida

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Title:
Modeling the effects of hydrodynamics, suspended sediments, and water quality on light attenuation in Indian River Lagoon, Florida
Series Title:
Modeling the effects of hydrodynamics, suspended sediments, and water quality on light attenuation in Indian River Lagoon, Florida
Creator:
Christian, David Joseph
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
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English

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University of Florida
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University of Florida
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Full Text
UFIJCOEI-20Oj / / q

MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA

by
DAVID JOSEPH CHRISTIAN

THESIS
2001

Coastal & Oceanographic Engineering Program
Department of Civil & Coastal Enierg 433 Weil Hall -P.O. Box 116590 Gaievle Florida 32611-6590




UFL/COEL-2001/017

MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA
by
DAVID JOSEPH CHRISTIAN

THESIS

2001




MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION
IN INDIAN RIVER LAGOON, FLORIDA
By
DAVID JOSEPH CHRISTIAN

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

2001




Copyright 2001
by
David Joseph Christian




I dedicate this thesis to my family, whose love and support have helped me get to where I am.




ACKNOWLEDGMENTS

I would like to thank the chairman of my committee, Dr. Peter Sheng, for his support and guidance throughout my master's study. I would also like to thank the other members of my committee, Dr. Robert Dean and Dr. Edward Phlips, for their help and insight.
The St. Johns River Water Management District funded the IRLPLR (Indian River Lagoon Pollutant Load Reduction) model development project, which provided me the opportunity to study light attenuation processes in the IRL. I need to extend a special thank you to Justin Davis, Haifang Du, Detong Sun, Chenxia Qiu, and all of Dr. Sheng's other students for their help and friendship. I am also indebted to Adam Kornick who started the light attenuation work. I also cannot thank Dr. Chuck Gallegos enough for providing information on his model and answering my long list of questions. A big thank you goes out to the crew at the coastal lab, Sidney, Vik, Vernon, Chuck, and J. J., for helping with field and lab work and being understanding when we brought something back from the field broken. I would also like to thank Terry Johnson for helping with my diving.
Finally, I need to thank Kim Christmas for her friendship, support, and love. I could not have made it without her.




TABLE OF CONTENTS
Pagye
ACKNOWLEDGMENTS............................................. iv
LIST OF TABLES .................................................. ix
LIST OF FIGURES................................................. xv
ABSTRACT ...................................................... Xxi
1 INTRODUCTION AND BACKGROUND.............................. 1
1. 1 Introduction and Background ........................................ 1
1.2 Light Definitions ................................................. 6
1.3 Seagrass and PAR Relationships .................................... 13
1.4 Previous Light Attenuation Models................................... 15
1.5 This Study ..................................................... 18
2 DATA SETS ................................................... 20
2.1 Introduction .................................................... 20
2.2 Sampling Procedures............................................. 20
2.2.1 SERC Data Set........................................... 20
2.2.2 UE Data Set............................................. 22
2.2.3 WQMN Data............................................ 25
2.2.4 HBOI Data.............................................. 25
2.2.5 Phlips Data ............................................. 27
2.3 Data Set Statistics ............................................... 28
2.3.1 SERC Data Set .......................................... 28
2.3.2 UE Data Set............................................. 29
2.3.3 WQNData Set......................................... 30
2.3.4 HBOI Data Set........................................... 31
2.3.5 Phlips Data Set........................................... 33
2.3.6 All Data Sets Comparison .................................. 33
V




2.4 The Relative Importance of Various Factors for Light Attenuation ............. 34
2.4.1 Equations Used to Calculate Kd(PAR) Attributable to Each Variable .... 35 2.4.2 D ata Set Analysis ............................................ 36
2.4.3 Percentage of Each Measured Kd(PAR) Due to Each Variable ......... 37
2.4.4 Analysis by Section .......................................... 42
2.4.5 Analysis by Season .......................................... 43
2.5 D ata D ifferences .................................................... 45
2.5.1 U F D ata ................................................... 46
2.5.2 W QM N D ata ............................................... 47
2.5.3 BB O I D ata ................................................. 51
2.5.4 Attempt to Make TSS Data Uniform ............................. 55
2.6 Data Sets Statistics With Converted TSS Values ........................... 57
2.6.1 Converted TSS Data Sets ...................................... 57
2.6.2 Season's Statistics ........................................... 58
2.6.3 Section's Statistics ........................................... 59
3 REGRESSION M ODELS ............................................. 64
3.1 Introduction ...... 64
3.2 Regression M odel Statistics ........................................... 66
3.3 Regression Models for Various Data Sets ................................ 69
3.3.1 Best One-Variable Linear Regression Model for Each Data Set ........ 69
3.3.2 Best Two-Variable Linear Regression Model for Each Data Set ....... 71 3.3.3 Best Three-Variable Linear Regression Model for Each Data Set ...... 72 3.3.4 Best Three Variable Factorial Regression Model for Each Data Set ..... 76 3.4 Best Regression Models for Seasonal Data Sets ............................ 77
3.4.1 Best One-Variable Linear Regression Model for Each Season ......... 77
3.4.2 Best Two-Variable Linear Regression Model for Each Season ......... 80
3.4.3 Best Three-Variable Linear Regression Model for Each Season ........ 81
3.4.4 Best Three-Variable Factorial Regression Model for Each Season ...... 82 3.5 Best Regression Models for Each Section of the IRL ........................ 83
3.5.1 Best One-Variable Linear Regression Models for Each Section ........ 83
3.5.2 Best Two-Variable Linear Regression Model for Each Section ........ 85
3.5.3 Best Three-Variable Linear Regression Model for Each Section ....... 87 3.5.4 Best Three-Variable Factorial Regression Model for Each Section ..... 88 3.6 Summary of Regression M odels ........................................ 89
4 NUMERICAL M ODEL .............................................. 91
4.1 Introduction ........................................................ 91
4.2 K irk's W ork ....................................................... 91
4.3 G allegos's W ork .................................................... 93
4.3.1 Absorption by W ater ......................................... 94




4.3.2
4.3.3
4.3.4
4.3.5
4.3.6
4.3.7
4.4 PARPS

Absorption by Yellow Substance .......... Absorption by Phytoplankton............
Absorption by Detritus ............. ...
Scattering by Particles .................
Use of Absorption and Scattering Coefficients Gallegos's Calibration for Use in the IRL .. M odel . . . . . . . .

....94
....96
....96
....97
....98
.. .100
... 102

5 NUMERICAL MODEL OF LIGHT ATITENUATION ......

5.1 Introduction ................................................... 105
5.2 Debugging .................................................... 106
5.3 Individual Data Set Runs ......................................... 106
5.3.1 Full Collected Data Sets ................................... 107
5.3.2 Data Sets by Season ...................................... 116
5.3.3 Data Sets of Sections ..................................... 117
5.4 Alternate Model Coefficients ...................................... 120
5.4.1 Each Season's Coefficients................................. 128
5.4.2 Each Section's Coefficients ................................ 132
5.4.3 Comparison of Monte Carlo Coefficients to Experimental Coefficients 140

5.5 Alternate TSS-Turbidity Relationships

... . . .. . . . .140

6 IN4TEGRATED MODEL RESULTS .............................
6.1 Introduction ................................................
6.2 Model Architecture ..........................................
6.2.1 Allparpsworkch3d.f...................................
6.2.2 Light Calculations....................................
6.3 Segment Analysis ............................................
6.3.1 Comparison to Data ...................................
6.3.2 Time Series Analysis ..................................

7 CONCLUSIONS......................

... . . . . . .174

7.1 Data Sets...................
7.2 Individual Light Attenuation Models 7.3 Integrated Light Attenuation Model 7.4 Future Work .................
APPENDIX A ..................

APPENDIX B .................................................... 187

.145 .145 .146 .147 .156 .157 .158

.... 174
.... 175
.... 177
... 178




A PPEND IX C ........................................................ 190
LIST OF REFERENCES ................................................ 203
BIOGRAPHICAL SKETCH ............................................. 207




LIST OF TABLES

Table Page
2.1. Sample sites used in the SERC study .................................. 21
2.2. SERC water quality variables used in the light attenuation model ............ 22
2.3. UF synoptic sampling trips were carried out on these dates ................. 23
2.4. UF water quality variables used in the light attenuation model ............. 23
2.5. Sample sites used during UF synoptic sampling trips ................... 24
2.6. Additional sampling sites used during UF sampling trips 1-6 ............... 25
2.7. Sites sampled during WQMN sampling trips ............................ 26
2.8. HBOI water quality variables used in the light attenuation model ............ 27
2.9. Sample sites used during the HBOI study ............................... 27
2.10. Data set statistics for the data collected during the SERC study ............ 28
2.11. Statistics for the data collected during UF synoptic sampling
trips 1-6 ........................................................ 29
2.12. Statistics for the data collected during UF synoptic sampling trips 7-12 without
transform ed TSS ................................................ 30
2.13. Data set statistics for data collected by WQMN from March 1996
through 1998 .................................................... 31
2.14. Data set statistics for data collected by WQMN between March and May 1999
without transform ed TSS .......................................... 31
2.15. Data set statistics for HBOI data collected during HBOI's first sampling year
without transformed TSS ....................................... 32




2.16. Data set statistics for HBOI data collected during HBOI's second sampling
year without transformed TSS ...................................... 32
2.17. Data set statistics for data collected by Phlips during their October 1999
sampling trip in which TSS data were collected .......................... 33
2.18. Mean values of variables of interest from each of the data sets used in this
study without transformed TSS data ................................... 34
2.19. Percent of Kd(PAR) due to each attenuator in this study ................. 37
2.20. Percentage of Kd(PAR) due to color, chlorophyll a, and tripton for each
data set for Kd(PAR) values above and below 1.00 m1 ..................... 40
2.21. Percentage of Kd(PAR) due to color, chlorophyll a, and tripton for each data
set for Kd(PAR) values above and below the mean Kd(PAR) value for each
data set ........................................................ 4 1
2.22. Percent of Kd(PAR) due to color, chlorophyll a, and tripton for each
section of the IRL ................................................ 43
2.23. Percent of Kd(PAR) due to color, chlorophyll a, and tripton for
each season ..................................................... 44
2.24. Turbidity calculations using HBOI years 1 and 2 average TSS values ......... 54
2.25. Kd(PAR) calculations using HBOI years 1 and 2 average TSS values ........ 54 2.26. Results from TSS split sample analysis ................................ 56
2.27. Transformed TSS statistics using WQMN 1994-1998 and WQMN 1999
turbidity-TSS relationships .......................................... 58
2.28. TSS statistics for data transformed using WQMN 1994-1998 and WQMN
1999 turbidity-TSS relationships .................................... 59
2.29. Statistics for January March with transformed TSS values .............. 60
2.30. Statistics for April June with transformed TSS ...................... 61
2.31. Statistics for July September with transformed TSS ................... 61
2.32. Statistics for October December with transformed TSS ................... 61




2.33. Statistics for the South Section of the JRL with transformed TSS ............62
2.34. Statistics for the Middle Section of the LRL with transformed TSS ...........62
2.35. Statistics for the North Section of the TRL with transformed TSS ............62
2.36. Statistics for the Banana River with transformed TSS .................... 63
2.37. Statistics for the Mosquito Lagoon with transformed TSS ................. 63
3.1. Best one-variable regression model for each data set.................... 70
3.2. F values and p values for the best one-variable regression models ........... 71
3.3. Best two-variable model for each data set ............................. 72
3.4. F values and p values for the best two-variable regression models ........... 73
3.5. Best three-variable regression model for each data set................... 74
3.6. R 2 values for the best three-variable model for each data set and the
improvement in R 2 over the two- variable model....................... 74
3.7. F values and p values for each variable in three-variable regression models.
....................................................... 75
3.8. R 2 values for the best three-variable factorial model for each data set
and the R 2 improvement over the best three-variable regression model for each
data set ..................................................... 76
3.9. Best three-variable factorial model for each data set..................... 78
3.10. Best one-variable model for each season .............................. 79
3.11. F values and p values for each season's best one-variable model ............ 80
3.12. Best two-variable model for each season .............................. 80
3.13. F values and p values for each season's best two variable model ............ 81
3.14. Best three variable model for each season ............................. 81




3.15. R 2 for the best three variable regression model for each season and the R 2
improvement over the best two variable models........................ 82
3.16. F values and p values for each season's best three variable regression model. . 82
3.17. R' for the three variable factorial model for each season and the R 2
improvement over the three variable regression models.................. 83
3.18. Best three variable factorial model for each season ...................... 84
3.19. Best one-variable regression model for each section..................... 85
3.20. F values and p values for the best one-variable regression model for
each section.................................................. 85
3.21. Best two-variable regression model for each section..................... 86
3.22. F values and p values for the best two-vari able model for each section ........86
3.23. Best three-variable regression model for each section.................... 87
3.24. R 2 for the best three-variable regression model for each section and the R 2
improvement over the best two-variable model for each section ............87
3.25. F values and p values for the best three-variable regression model for each
section...................................................... 88
3.26. R 2 for each section's best three-variable factorial model and the R 2
improvement over the best three-variable regression model for each section. ..89 3.27. Best three-variable factorial model for each section..................... 90
4.1. Absorption by water per wavelength................................ 95
4.2. Absorption by chlorophyll per wavelength ........................... 97
4.3. Spectral incident PAR values..................................... 100
4.4. Gallegos's model coefficients for the Marker 198 sample site ............. 101
4.5. Gallegos's model coefficients for the Ft. Pierce Inlet sample site ........... 101
4.6. Kornick's model coefficients for the entire IRL....................... 104




5.1. RMS errors (m-) of Kd(PAR) for numerical model runs using Marker 198
coefficients and Ft. Pierce coefficients ................................ 107
5.2. Mean Standard Deviation (mi) from model results and data for each
data set ....................................................... 10 8
5.3. RMS errors (m-1) for numerical model runs for each season using Marker 198
coefficients and Ft. Pierce coefficients ................................ 116
5.4. Mean Standard Deviation (m') from model results and data for
each season ..................................................... 117
5.5. RMS errors (m') of Kd(PAR) for numerical model runs for each section
using Marker 198 coefficients and Ft. Pierce coefficients ............... 120
5.6. Mean and Standard Deviation (m') of Kd(PAR) from model results and data
for each section ................................................. 121
5.7. Coefficient ranges for use in Monte Carlo model ........................ 125
5.8. Results for SERC One Thousand Run Monte Carlo Tests With sy = 0.016, ... 126
5.9. Comparison of RMS errors for each data set using Ft. Pierce coefficients and
SERC monte carlo coefficients with sy = 0.0160 ........................ 127
5.10. Comparison of means standard deviations (in1) for Kd(PAR) from data,
model results with Ft. Pierce coefficients, and SERC monte carlo coefficients
w ith sy = 0.0160 ................................................. 128
5.11. Coefficients for each of the seasons found by Monte Carlo method ........ 133
5.12. Comparison of RMS errors of Kd(PAR) for model runs for each season
using the coefficients found by monte carlo method for each season, coefficients found by monte carlo method for the SERC set, and the
Ft. Pierce coefficients (m ') ......................................... 133
5.13. Comparison of mean and standard deviation of modeled Kd(PAR) values for
each season using the coefficient set determined for the SERC data set with
the monte carlo method, the Ft. Pierce coefficient set, and data (mi) ........ 133
5.14. Coefficients found for each section by monte carlo method ................ 137




5.15. Comparison of RMS errors for model runs for each section using the
coefficients found by monte carlo method for each section, coefficients
found by monte carlo method for the SERC set, and the Ft. Pierce
coefficients (m ") ............................................... 137
5.16. Comparison of mean and standard deviation of modeled Kd(PAR) values
for each section using the coefficient set determined for the SERC data set
with the monte carlo method, the Ft. Pierce coefficient set, and data (m-') .... 137
5.17. Comparison of RMS Error Values for the Northern IRL Data of Each Data Set
using Gallegos's Turbidity TSS Equation and the Turbidity TSS Equation
Found by Using WQMN 1996 1998 Sites 102, 107, and 110 ............. 144
6.1. Comparison of simulated results to modeled data for Segment 2 ........... 159
6.2. Comparison of simulated results to measured data for Segment 4 ........... 159
6.3. Comparison of simulated results and measured data for Segment 5 ......... 160
6.4. Comparison of simulated results and measured data for Segment 6 ......... 160
7.1. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each collected
data set ....................................................... 176
7.2. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each season of
the year ........................................................ 177
7.3. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each section of the
lagoon ........................................................ 177
A.1. Minimum, maximum, and mean values used for the model sensitivity tests. .. 180
C. 1. The Kd(PAR) (m) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
S ite 1 ......................................................... 193




C.2. The Kd(PAR) (m') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
S ite 2 ......................................................... 194
C.3. The Ka(PAR) (ml) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 3 ......................................................... 195
C.4. The Kd(PAR) (m') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 4 ......................................................... 196
C.5. The Kd(PAR) (m1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Ka(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
S ite 5 ......................................................... 197




LIST OF FIGURES

Figure Page
1.1. H alodule wrightii .................................................3
1.2. Syringodiumfiliforme .............................................3
1.3. Halophila englemanii..............................................4
1.4. Thalassia testudinum ..............................................4
1.5. Halophilajohnsonii and Halophila decipiens ............................ 5
1.6. Ruppia maritima .................................................5
1.7. The setup for a detector measuring radiance through an angle AD .......... 8
1.8. A 27r PAR sensor for measuring downward irradiance ................... 10
1.9. A 47t PAR sensor for measuring downward irradiance..................... 11
2.1. Percentage of Kd(PAR) due to chlorophyll a.......................... 38
2.2. Percentage of Kd(PAR) due to color ..................................38
2.3. Percentage of Kd(PAR) due to tripton .................................. 39
2.4. UF sampling trips 1-6 relationship between Kd(PAR) and TSS.............. 47
2.5. UF sampling trips 7-12 relationship between Kd(PAR) and TSS............. 48
2.6. WQMN 1996-1998 relationship between Kd(PAR) and TSS................ 49
2.7. WQMN 1999 relationship between Kd(PAR) and TSS................... 50
2.8. WQMN 1996-1998 relationship between turbidity and TSS............... 50




2.9. WQMN 1999 relationship between turbidity and TSS ..................... 51
2.10. HBOI year 1 relationship between Kd(PAR) and TSS ................... 52
2.11. HBOI year 1 relationship between turbidity and TSS ...................... 53
2.12. HBOI year 2 relationship between Kd(PAR) and TSS ................... 53
2.13. HBOI year 2 relationship between turbidity and TSS ...................... 54
5.1. Model results for all data sets using Ft. Pierce coefficients ............... 109
5.2. Model results for all data sets using Marker 198 coefficients ............. 109
5.3. Model results for SERC data set using Ft. Pierce coefficients .............. 110
5.4. Model results for SERC data set using Marker 198 coefficients ........... 110
5.5. Model results for UF synoptic trips 1-6 using Ft. Pierce coefficients ......... 111
5.6. Model results for UF synoptic trips 1-6 using Marker 198 coefficients ....... 111 5.7. Model results for UF synoptic trips 7-12 using Ft. Pierce coefficients ........ 112
5.8. Model results for UF synoptic trips 7-12 using Marker 198 coefficients ...... 112 5.9. Model results for WQMN 1996 1998 using Ft. Pierce coefficients ......... 113
5.10. Model results for WQMN 1996-1998 using Marker 198 coefficients ....... 113 5.11. Model results for WQMN 1999 using Ft. Pierce coefficients ............. 114
5.12. Model results for WQMN 1999 using Marker 198 coefficients ............. 114
5.13. Model results for BOI Year 2 using Ft. Pierce coefficients ............... 115
5.14. Model results for BOI Year 2 using Marker 198 coefficients ............ 115
5.15. Model results for January March data using Ft. Pierce coefficients ......... 118
5.16. Model results for April June data using Ft. Pierce coefficients ........... 118
5.17. Model results for July September data using Ft. Pierce coefficients ....... 119

xvii




5.18. Model results for October December data using Ft. Pierce coefficients. .. .119 5.19. Model results for the south section of the IRL using Ft. Pierce coefficients. ..121
5.20. Model results for the middle section of the IiRL using Ft. Pierce
coefficients.................................................. 122
5.21. Model results for the north section of the IiRL using Ft. Pierce coefficients. . 122 5.22. Model results for Banana River using Ft. Pierce coefficients .............. 123
5.23. Model results for Mosquito Lagoon using Ft. Pierce coefficients ........... 123
5.24. Graph of Equation 4. 10. Circles are the Ft. Pierce Inlet data, and squares
are the Marker 198 data......................................... 124
5.25. Model results for all data sets using SERC Monte Carlo coefficients ........ 129
5.26. Model results for the SERC data set using SERC Monte Carlo
coefficients.................................................. 129
5.27. Model results for UF synoptic trips 1-6 using SERC Monte Carlo
coefficients.................................................. 130
5.28. Model results for UF synoptic trips 7-12 using SERC Monte Carlo
coefficients.................................................. 130
5.29. Model results for WQMN 1996-1998 using SERC Monte Carlo
coefficients.................................................. 131
5.30. Model results for WQMN 1999 using SERC Monte Carlo coefficients ...... 131 5.31. Model results for HiBOI Year 2 using SERC Monte Carlo coefficients .......132
5.32. Model results for January March data using SERC Monte Carlo
coefficients.................................................. 134
5.33. Model results for April June data using SERC Monte Carlo coefficients. ..135
5.34. Model results for July September data using SERC Monte Carlo
coefficients.................................................. 135

xviii




5.35. Model results for October December data using SERC Monte Carlo
coefficients.................................................. 136
5.36. Model results for the south section of the IIRL using SERC Monte Carlo
coefficients.................................................. 138
5.37. Model results for the middle section of the IRL using SERC Monte Carlo
coefficients.................................................. 138
5.38. Model results for the north section of the IRL using SERC Monte Carlo
coefficients.................................................. 139
5.39. Model results for Banana River using SERC Monte Carlo coefficients .......139
5.40. Model results for Mosquito Lagoon using SERC Monte Carlo coefficients. ..140
5.41. Graph of Equation 4.10. Circles are the Ft. Pierce Inlet data, and
squares are the Marker 198 data. The solid line represents the curve
fitting the SERC "Monte Carlo" coefficients ......................... 141
5.42. Bottom sediment size (D50) from south to north in the IRL............... 142
6.1. Simulated TSS results used for calculating the light attenuation coefficient
for each i, j location in the grid including water quality and TSS loading....149
6.2. Simulated Chlorophyll a results used for calculating the light attenuation
coefficient for each i, j location in the grid including loading of water
quality and TSS .............................................. 150
6.3. Interpolated color values with loading used for calculating the light
attenuation coefficient for each i, j location in the grid including ........... 151
6.4. Depth of grid used to calculate the light attenuation coefficient, light at
the bottom of the grid, and percentage of incident light reaching the
bottom..................................................... 152
6.5. Simulated Kd(PAR) values throughout the IRL for a model run including
loading..................................................... 153
6.6. Simulated amount of light reaching the bottom of the grid for the case
including loading ............................................. 154




6.7. Simulated percentage of incident light reaching the bottom of the grid
for the loading case ............................................... 155
6.8. IRL segm ent locations ............................................. 157
6.9. One year time series plot of simulated TSS concentrations for segments
1-4 for three loading cases ........................................ 162
6.10. One year time series plot for simulated TSS concentrations for segments
5-8 for three loading cases ........................................ 163
6.11. One year time series plots of simulated chlorophyll a concentrations for
segments 1-4 for three loading cases ................................ 164
6.12. One year time series plots of simulated chlorophyll a concentrations for
segments 5-8 for three loading cases ............................... 165
6.13. One year time series plots of interpolated color for segments 1-4 for
three loading cases .............................................. 166
6.14. One year time series plots of interpolated color for segments 5-8 for
three loading cases .............................................. 167
6.15. One year time series plots of simulated Kd(PAR) for segments 1-4 for
three loading cases .............................................. 168
6.16. One year time series plots of Kd(PAR) for segments 5-8 for three
loading cases .................................................... 169
6.17. One year time series plots of simulated light at bottom for segments
1-4 for three loading cases ........................................ 170
6.18. One year time series plots of simulated light at bottom for segments
5-8 for three loading cases ........................................ 171
6.19. One year time series plots of simulated percent of incident light at
bottom for segments 1-4 for three loading cases ....................... 172
6.20. One year time series plots of simulated percent of incident light at
bottom for segments 1-4 for three loading cases ....................... 173




A. 1. Variation of predicted Kd(PAR) values with variations in chlorophyll a
concentration .................................................. 182
A.2. Variations in predicted Kd(PAR) values due to variations in color ......... 183
A.3. Variations in predicted Kd(PAR) due to variations in TSS concentration..... 183 A.4. Variations in predicted Kd(PAR) due to variations in TSS concentration..... 184 A.5. Variations in predicted Kd(PAR) due to variations in water depth ........... 184
A.6. Variations in predicted Kd(PAR) due to variations in time of day
between 1000 and 1400 .......................................... 185
A.7. Variations in predicted Kd(PAR) due to variations in time of day between 0800
and 1600 ...................................................... 185
A.8. Variations in predicted Kd(PAR) due to variations in day of the year ....... 186 B.1. Monte Carlo results for the SERC data set ............................. 188
B.2. Monte Carlo results for all data sets combined ......................... 189
C.1. Sites used for vertical grid cell tests .................................. 192
C.2. The amount of PAR calculated at each layer in the vertical grid at Site 1
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run ...... 198 C.3. The amount of PAR calculated at each layer in the vertical grid at Site 2
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run ...... 199 C.4. The amount of PAR calculated at each layer in the vertical grid at Site 3
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run ...... 200 C.5. The amount of PAR calculated at each layer in the vertical grid at Site 4
using multiple Ka(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run ...... 201




C.6. The amount of PAR calculated at each layer in the vertical grid at Site 5
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run ...... 202

xxii




Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION IN INDIAN RIVER LAGOON, FLORIDA By
David Joseph Christian
December 2001
Chairperson: Dr. Y. Peter Sheng Major Department: Civil and Coastal Engineering Department
Declining water quality due to anthropogenic effects has led to a decrease in seagrass biomass in coastal waters throughout the world. Seagrass beds are vital components of the coastal ecosystem providing both food and habitat to many species as well as acting as a stabilizer for marine sediment. The seagrass beds in the Indian River Lagoon (IRL), a shallow coastal lagoon along the East Coast of Florida, help to support a fishing industry with a local impact of a billion dollars a year. A decline in light reaching the seagrass due to poor water quality is suspected of being the major factor in seagrass loss in the IRL as well as elsewhere.
In order to better evaluate water management decisions aimed at increased seagrass growth in the IRL, the University of Florida has been developing an Indian River Lagoon

xxiii




Pollutant Load Reduction Model (IRL-PLR). This model integrates component models of hydrodynamic, water quality, sediment, seagrass, and light attenuation processes. This thesis focuses on the development of a light attenuation model and its integration into the IRLPLR model. First five different sets of water quality and light data for the IRL are examined. The report then evaluates regression, factorial, and numerical light attenuation models in order to select the best light attenuation component for incorporation into the JRL-PLR model. Each model includes the known light attenuators: suspended solids, chlorophyll a in phytoplankton, and color from dissolved organic matter. One, two, and three variable regression models, as well as a three variable factorial model were developed for each of the data sets, as well as each of the seasons of the year, and each of five sections of the IRL. The numerical model was calibrated for each data set, season, and section to test the robustness of the model and to see if incorporating spatial or temporal variations could improve model results.
Variations in each of the regression and factorial models make it difficult to find a single model, or a group of models, to best explain all of the data. One set of coefficients for the numerical model was found that works well with each of the data sets, seasons, and sections. The numerical model along with that set of coefficients was then incorporated into the IRL-PLR model.

xxiv




CHAPTER 1
INTRODUCTION AND BACKGROUND
1.1 Introduction and Background
The Indian River Lagoon (IRL), with more than two thousand identified species, is one of the most diverse estuaries in the world (Barile et al., 1987). Lying on the East Coast of Florida between Ponce de Leon Inlet in the north and Jupiter Inlet in the south, the IRL stretches 341 km with an average depth of 1.2 m and a width varying between 0.4 and 12.1 km (Steward et al., 1994).
Seagrass beds play an important role in the IRL, as in estuaries in general. They are highly productive and ecologically important habitats as well as important sediment stabilizers (Zieman, 1982). Seagrass beds provide food for fishes and invertebrates as well as protection from predators (Zieman, 1982). Because of these functions, the seagrass meadows in south Florida's coastal areas are possibly the greatest nursery and feeding areas in the region (Zieman, 1982). The importance of seagrass beds also influences water management decisions. Because of their sensitivity to water quality conditions, as well as their far reaching importance throughout the system, seagrass beds can act as a gauge for short and long term water conditions (Vimstein and Morris, 1996).
While currently there are between approximately 70,000 and 90,000 acres of seagrass beds in the IRL, this is a decrease from past years (Virnstein and Morris, 1996). Because of




2
their importance to sea life, the IRL seagrass beds are a foundation for the local fishing industry, which generates about a billion dollars a year (Virnstein and Morris, 1996). This works out to about $12,000/ year for each acre of seagrass coverage (Virnstein and Morris, 1996).
Seven species of seagrass are present in the IRL, giving it the highest diversity of seagrass species of any estuary in North America (Dawes et al., 1995; Virnstein, 1995). The seven species in order of decreasing abundance are: Halodule wrightii shoal grass
Syringodiumfiliforme manatee grass
Halophila engelmannii star grass
Thalassia testudinum turtle grass
Halophila decipiens paddle grass
Halophilajohnsonii Johnson's seagrass
Ruppia maritima widgeon grass
Halophilajohnsonii occurs only in the southern portion of the IRL. The other six species are the six species found in tropical and subtropical estuaries in the western hemisphere (Virnstein and Morris, 1996). These seagrass species are seen in Figures 1.1 1.7. Figures are from Florida Department of Environmental Protection (2001).
It is believed that the amount of photosynthetically active radiation (PAR), which is the portion of light usable by plants, reaching the seagrass beds is the main factor controlling the health of seagrass beds (Virnstein and Morris, 1996). Light attenuation in the water column limits the amount of PAR which reaches the seagrass. The main light attenuators in the water column are the water itself, dissolved yellow substance (color), phytoplankton, and suspended particulates (Kirk, 1981). A decline in water quality, causing an increase in a light attenuator, can lead to adverse effects on seagrass health.




Shoal-grass (Halodule wright) Figure 1.1: Halodule wrightii

Ma natee-grass
(Syrngodiurm iliforow)

Figure 1.2: Syringodiumfiliforme




Figure 1.3: Halophila englemanii

Turtle-grass (Thaassia testudinrnm)

Figure 1.4: Thalassia testudinum




24
N

Ig

)ohnson's Sea-grass (Halophila johnsonii)

Paddle-grass
(Halophi a decipiens;

Figure 1.5: Halophilajohnsonii and Halophila decipiens

Figure 1.6: Ruppia maritima




6
The University of Florida, with funding from the St. Johns River Water Management District (SJRWMD), is developing a pollutant load reduction model for the Indian River Lagoon (IRL-PLR) to help in making water management decisions (Sheng, 1999). The IRLPLR model integrates hydrodynamic, water quality, sediment transport, light attenuation, and seagrass models in order to predict changes in water quality and seagrass growth due to changes in nutrient loading. For the reasons outlined above, light attenuation plays a major role in the seagrass health, and therefore a robust light attenuation component of the model is vital to the overall success of the IRLPLR model. The goal set forth by the SJRWMD is to be able to consistently have seagrass growth out to a depth of 1.7 m (Virnstein and Morris, 1996). The light attenuation model is an important tool for finding where this is possible and what water quality changes are needed in order to allow this to happen. This thesis examines the available light and water quality data for the IRL along with regression, factorial, and numerical models in order to select and incorporate a calibrated light attenuation model into the overall IRL-PLR model.
1.2 Light Definitions
Photon
To better understand what is being discussed here, a few definitions for light are needed. Light is composed of electromagnetic energy packets called photons. The photons contain properties of both a wave and a particle in what is known as a wave-particle duality. Each photon carries a certain amount of radiant energy (Mobley, 1994). The amount of energy q contained in a photon is related to the frequency of the wave V, and its corresponding wavelength A by the speed of light c and Planck's

constanth = 6.626x 10-34 J S:




hc
q= hv=7 A (1.1)
When we measure light, what the detector is actually measuring is the radiant energy or the actual number of photons which are hitting it. Thermal detectors measure the heat which comes from absorbing the photon's radiant energy. Quantum detectors measure the number of photons which are hitting them. Quantum detectors were used in this study. Often a diffuser will be placed in front of the detector so that only certain wavelengths will be detected. In this case, a diffuser was used so that only wavelengths between 400 nm and 700 nm (the visible spectrum) would be measured. Radiance
If a tube is put in front of the detector (Figure 1.7), such that the light being measured is only allowed to enter the detector through a certain angle A i the radiance L is being measured. The equation which shows this measurement is: L ; )- A Q UJs-'m-' sf 1 nm-1) (1.2)
A tAAA A A
in which A Q is the amount of radiant energy the detector is exposed to, A t is the time which the detector is exposed to the light, AA is the area of the diffuser that the light is passing through to get to the detector, and A A is the wavelength interval which the diffuser is allowing to pass through. L is shown as a function of which the location of the instrument in the water, t is time, is the direction of the light, and A is the wavelength at

the center of the wavelength interval A A2.




Filter A%
DiffuDr AA
Collecting Tube
Figure 1.7: The setup for a detector measuring radiance through an angle
AQ (Adapted from Mobley, 1994).
If everything on the left side of Equation 1.2 is taken to be infinitesimally small, then the integral may be taken and Equation 1.2 becomes: d~tdAd oQ (W M-2 sr'1 nm1) (1.3)
Radiance can be used to find the other needed radiometric values since it includes all of the information needed about the light field, such as wavelength, spatial features, temporal features, and directional features.
Since we want to know how much light is available to plants, it is important to know how much light is coming down from all angles, not just the small angle A 2 To measure this, the tube which was in front of the detector in Figure 1.7 is removed allowing light to reach the diffuser from all angles above it and irradiance is measured.




Downward Radiance
Since this study is only concerned with the light which is coming from the sun, and not that which is being reflected from the bottom of the estuary, the collectors are setup facing the water surface in order to measure downward irradiance. The equation for downward irradiance is then:
AQ
Ed (;t;2)- (W M- nm-1). (1.4)
AtAAA2
This is the same as the equation which explains radiance, except it now does not include the angle A 2 since the light being measured is not being confined to just the one small angle. Irradiance Sensors
There are two types of irradiance sensors. The first is a 2nr sensor as shown in Figure 1.8. If this type of sensor is pointed upward, then it is measuring spectral downward plane irradiance. If a beam of light is coming in incident to the sensor, and if the sensor is of area AA, the entire area, AA, is being illuminated by the beam. If the beam is coming in at angle 0, then the beam is only illuminating an area of AA cos 6. Since the collectors are collecting photons from all of the angles between 7t and 27, they are integrating the radiance L multiplied by IcosOI over all O's between it and 21t. For this study in which sunlight is being considered, puo is used in place of 0. The downward plane irradiance being measured is then related to the radiance as follows:
2 7r
Ed(x;t;7) = t f L(x ;t; 0; 0;A)cost sin WdWd (1.5)
0=00 =2;r




Diffuser
Filter
Detector
Figure 1.8: A 27t PAR sensor for measuring downward
irradiance (Adapted from Kornick, 1998).
The second type of irradiance sensor is the 4it sensor (Figure 1-9). Unlike the 2t sensor, the 47t will collect photons from all angles equally. In order to just capture the downward irradiance, a shield ( as seen in Figure 1-9) is needed to block any reflected light coming up from below. Since all angles are being collected, the measurement is of spectral downward scalar irradiance, Eod. The relationship between this measurement and the spectral radiance is shown in:
27 ;r/2
Eo (X; t;) A f L(Y;t;O;O;A)sinOdOdd (1-6)
Since the goal here is to find the light which is available for photosynthesis by phytoplankton and seagrass, then the concern is with the photosynthetically active radiation (PAR). Photosynthetically active radiation for phytoplankton includes both visible




Figure 1.9: A 47r PAR sensor for measuring downward irradiance.
wavelengths and near ultraviolet wavelengths. Since the near ultraviolet wavelengths are quickly absorbed in the water column, PAR is usually estimated as just the visible wavelengths between 400 nm and 700 nm (Mobley, 1994). This estimation is used in this study.
Downward PAR and Light Attenuation Coefficient
The downwelling PAR reaching the bottom, or any depth in the water column, is found using the Lambert Beer equation, I = Io*exp(-K(PAR)*z) (1-7)




12
where z is the depth below the water surface, Iz is the PAR at depth z, 10 is the PAR just below the water surface, and Kd(PAR) is the light attenuation coefficient for downward PAR (Dennison et al., 1993). The Lambert-Beer equation follows a negative exponential due to the nature of light attenuation in water. The wavelengths which are strongly absorbed disappear quickly as the light enters the water. As the easily absorbed wavelengths disappear, only the weakly absorbed wavelengths remain (Kirk, 1984). Therefore, if a light attenuation coefficient is calculated in the upper portion of the water column it will tend to be higher than if it is calculated, with the same water quality conditions, using a greater depth (Kirk, 1984).
Kd(PAR) is calculated from PAR measurements in the data by using the rearranged form of the Lambert-Beer equation,
This rearranged equation can be used to calculate Kd(PAR) using two measurements of PAR, I, and 10 a distance of z depth apart. It can also use multiple points to calculate Kd(PAR) as
the slope of the best fit line resulting from the plot of 1n( -fjZ vs z where 10 is the uppermost
PAR measurement and Iz is the PAR measurement at corresponding z depth below where 10 is measured.




13
In order to model the amount of PAR throughout the water column, Kd(PAR) is modeled and then used in Beer's Law along with the PAR at the water's surface to calculate PAR at the desired depths.
1.3 Seagrass and PAR Relationships
The minimum light requirements for submerged aquatic vegetation vary from 4 29% of the light just below the water surface (Dennison et al., 1993). For comparison, land plants in shaded areas require only 0.5 2% of the light just under the canopy (Hanson et al., 1987; Osmond et al., 1983). Phytoplankton and benthic algae also require much lower light levels. Green algae requires 0.05 1.0 % of incident light, while brown algae requires 0.7 1.5% of incident light (Luning and Dring, 1979). Crustose red algae requires as little as 0.0005% of incident light (Littler et al., 1985), while lacustrine and marine phytoplankton need 0.5 1.0% of incident light (Parsons et al., 1979; Wetzel, 1975). The higher respiration requirements of seagrasses have been pointed to as the reason for greater light requirements for seagrasses than for phytoplankton (Dennison, 1987).
Light requirements vary between species. Halodule wrightti and Syringodium filiforme have been found to each require 17.2% of incident light in Florida (Dennison et. al. From personal communication with W. J. Kenworthy, 1993). Another report puts the light requirement for S.filiforme in Florida at 18.3% of incident light (Duarte, 1991). Thalassia testudinum in Florida has been found to require 15.3% of incident light (Duarte, 1991). Kenworthy (1993) found much higher light requirements for H. wrightti and S.filiforme. His results show a minimum of 27% of surface light needed in Jupiter Sound and 35% in Hobe Sound. The Indian River Lagoon has a mild sloping bottom with a slope of about 2 cm m (Kenworthy, 1992). A gentle slope means that such a great range of light requirements could




14
mean a difference of many acres of seagrass. The same is true for changes in Kd(PAR) (Kenworthy, 1993).
Dennison (1987) found that Zostera marina L. requires an average of 12.3 hours a day of light above the light compensation point. The light compensation point is the light level at which the oxygen the plant is getting from photosynthesis is equal to the amount of oxygen it needs for respiration (Tomasko, 1993).
Duarte (1991) developed a relationship between compensation depth and the light attenuation coefficient using data for thirty seagrass species and Ruppia. The equation he developed is:
Z, = 1.86 / K (1-9)
in which ZC is the compensation depth and K is the light attenuation coefficient. This equation compares well with similar equations. Dennison (1987) found a similar equation for Zostera marina in the northeast United States. This is shown in Equation 1-10.
Z, = 1.62 / K (1-10)
Nielson et al. (1989) developed a similar equation for Z. marina in Danish estuaries as seen in Equation 1.11.
Z, = 1.53/K (1.11)
Vicente and Rivera (1982) developed an equation for T. testudinum in Puerto Rican waters. Their equation is Equation 1.12.
Z, = 1.36/K (1.12)




15
All of these relationships show the strong correlation between the depth at which seagrass will grow and light attenuation.
More recently, Fong et al. (1997), Cerco et al. (2000), and Burd and Dunton (2001) have developed seagrass models in which light is a major component in calculating seagrass growth and death. Fong et al. and Cerco used light in conjunction with salinity, temperature, and nutrients to model seagrass. Burd and Dunton had their model driven by the light reaching the seagrass.
1.4 Previous Light Attenuation Models
McPherson and Miller (1994) modeled attenuation in Tampa Bay and Charlotte Harbor by partitioning Kd(PAR) into portions due to water, color, chlorophyll a, and nonchlorophyll suspended matter as in Equation 1.13: k = kw + E2 C2 + E3 C3 + E4 *C4 (1.13)
where kw is the light attenuation due to water; E2, E3, andE4are the attenuation coefficients for dissolved matter, chlorophyll a, and nonchlorophyll suspended matter, respectively; C2 is water color (Pt-Co units); C3 is chlorophyll a concentration (mg m-3); and C4 is the nonchlorophyll suspended matter concentration (mg m3).
McPherson and Miller (1987) also found the percent contribution of each component to Kd(PAR) for Charlotte Harbor, Florida. Their findings include non-chlorophyll suspended matter accounting for 72.5% of Kd(PAR), dissolved matter accounting for 21%, suspended chlorophyll 4%, and water 3%. Phlips et al. (1995) found percent contributions in Florida Bay. Their results show non-chlorophyll suspended matter accounting for 75% of Kd(PAR), chlorophyll containing particles accounting for 14%, color accounting for 7%, and water accounting for 4%.




16
Hogan (1983) used a model which took into account the Raleigh scattering of photons by water molecules and Mie scattering from hydrosols as well as absorption. He found that absorption dominates attenuation for most of the spectrum, except in the visible spectrum, where scattering becomes most important between 350 nm and 500 nm. While the maximum transmission of light occurs at 465 nm in clear water, the maximum transmission in turbid waters occurs at about 550 nm. This is caused by suspended particulate matter absorbing and scattering more of the shorter wavelengths. Because of this, total transmittance decreases in turbid waters and the maximum transmittance occurs at the higher wavelengths (Hogan, 1983).
Kirk (1984) used Monte Carlo simulations in order to describe the apparent optical property of the light attenuation coefficient using the inherent optical properties of absorption and scattering. Through his Monte Carlo simulations, Kirk developed the equation: Kd = + G(,uo)ab]j (1.14)
in which Kd is the vertical light attenuation coefficient for downwelling irradiance, p0 is the cosine of the solar zenith angle, at is the total absorption within the water, and b is the scattering. G(,uo) is a function of/10 in which:
a(P.)= glVO0- 92 (1.15)
where g, and g2 are numerical constants which depend on the optical depth of interest. Kirk (1984) calculated values for g, and g2 for depths in which the downward irradiance in the




17
water is reduced to 10% of its subsurface value (the midpoint of the photic zone), and for where downward irradiance is 1% of its subsurface value. Kirk (1991) has found that Equation 1. 14 can be applied to most coastal water bodies studied by oceanographers.
Gallegos developed a physics based model for light attenuation (Gallegos and Correll, 1990; Gallegos, 1993; Gallegos and Kenworthy, 1996). His model uses Equations 1. 14 and 1.15 developed by Kirk (1984). The model calculates Kd(PAR) in five nm increments throughout the wavelength interval of interest. It can be used throughout the visible spectrum to find the attenuation coefficient for PAR, or can be used for the photosynthetically usable radiation (PUR) for a certain plant species. a, is found by summing the absorption by color, chlorophyll a, water, and detritus. Absorption by water is read in from a file for each wavelength of interest. Absorption due to the other components are calculated from equations. Scattering, b, is calculated for turbidity. a, and b are then used to calculate K12A) for each A used. Kd/2), along with incident light at that wavelength are then used to calculate the light at the depth of interest using the Lambert-Beer equation at that wavelength. The incident light and light at depth are each integrated over the wavelength interval of interest and used in a rearranged form of the Lambert-Beer equation to calculate Kd(PAR) over the wavelength interval. Tests by Gallegos have shown this model to work as well as Kirk's (Gallegos, 2001).
Gallegos has calibrated and used his model in the Rhode River and Chesapeake Bay (Gallegos and Correll, 1990). He then calibrated and used the model near Ft. Pierce, FL in the JRL (Gallegos, 1993; Gallegos and Kenworthy, 1996). The results show a coefficient of variation of around 15%. He notes, and it is important to remember here as well, that the




18
observed Kd(PAR) values also contain error which contributes to the variation between modeled and observed values.
There are a few advantages to Gallegos's model. The first is that it is based on physics with coefficients that can be calibrated to the area of interest. There are only four coefficients which need to be considered. Three are used to determine the absorption by detritus, while the fourth is used to calculate absorption by color. The next advantage is that the use of the Lambert-Beer equation enables depth to be included in the calculation. The model used by McPherson and Miller does not allow for this. Another advantage to Gallegos's model is that it can easily be adapted to calculate the attenuation coefficient for PUR as opposed to PAR for use with a specific plant species.
1.5 This Study
Two approaches have been taken here to finding the best model for Kd(PAR) given the current data sets. The first approach has been to develop a numerical model based on the work of Gallegos (1993) in the Indian River Lagoon. The second approach has been to develop a step-wise regression model using the PROC REG procedure in SAS software. For both of these approaches, total suspended solids, chlorophyll a (chl-a), and color were used in the prediction of Kd(PAR).
Chapter 2 describes the data sets used in this thesis. It also gives the statistics on the data sets used. Chapter 3 shows the regression models developed for the different data sets, segments of the IRL, and different seasons of the year. Chapter 4 outlines the numerical model used including the equations and background. Chapter 5 takes that one step further and describes the stand alone light attenuation model used for testing. This also includes calibration which was done for the model and results of test runs. Chapter 6 explains the




19
coupling of the light attenuation model to the rest of the IRLPLR model. It includes results of runs for 1998 with regular loading of nutrients and zero loading of nutrients. Chapter 7 includes discussion and conclusions for this thesis.




CHAPTER 2
DATA SETS
2.1 Introduction
Data sets from five sources are used in calibration and verification of the IRL-PLR light attenuation model. All five data sets include both light data as well as water quality data. The five data sets include data taken by Gallegos of the Smithsonian Environmental Research Center (SERC) for calibration of his numerical model (Gallegos, 1993), data collected by UF during twelve synoptic sampling trips in 1997-1998, Water Quality Monitoring Network Data (WQMN) received from SJRWMD, and data collected by Hanisak at Harbor Branch Oceanographic Institute (HBOI). Data collected Phlips (2000) for the IRLPLR project are also used.
2.2 Sampling Procedures
The following section outlines the sample sites for each of the data sets. When available, equipment used for sampling are also shown. Data from the different groups cover 1994-1999.
2.2.1 SERC Data Set
Gallegos (1993) sampled light and water quality concurrently near Ft. Pierce Inlet for calibration of a light attenuation model for the southern part of the IRL. No set frequency was used for the sampling, but sampling occurred over several days in December, 1992; and March and April of 1993.




21
Light sampling was done measuring downwelling PAR using 27r Licor 192B underwater quantum sensors. Sampling was done over the visible spectrum, with the spectrum being divided into 5 nm increments by interference filters. A deck cell on board the boat was used to normalize each channel of the spectral radiometer (Gallegos, 1993a). Vertically integrated water samples were used for the water quality. They were sampled using a 2 liter Labline Teflon bottle. For sampling, the bottle was slowly lowered, and then brought back up more rapidly than it could fill. An initial sample was used for rinsing in the field. Once rinsed, multiple samples were taken each day at each station. The laboratory methods used were submitted to the FDEP in a Research Quality Assurance Plan by Gallegos (1993a). The locations for SERC sampling are shown in Table 2. 1, while the water quality sampling relevant to the light attenuation model is shown in Table 2.2.
Table 2. 1: Sample sites used in the SERC study. Site Latitude N Longitude W Northing UTM Easting UTM
___ ___(in) (in)
Ft. Pierce Inlet 270 28'06.0" 800 19'5 1.0" 3038522 566137
Taylor Creek,
Near Channel
Marker 184
Near Channel 270o22' 16.8~ 800 16'38.4" 3027807 571486
Marker 198
Near anlInlet 270 28'03.6" 800 18'58.8" 3038456 567570
Range MarkerII
Taylor Creek Furthest location upstream that could be reached. Designated Upstream C-25 C-25 since Taylor Creek receives flow from canal structure C-25. Channel Marker Near the entrance to Harbor Branch Oceanographic Institute. 1721
Near Marker 186 1Near Ft. Pierce Inlet in turning basin.




Table 2.2: SERC water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle I Pg/L chl-a

2.2.2 UF Data Set
UF conducted twelve synoptic sampling trips between April, 1997 and May, 1998 (Sheng and Melanson, 1999). The first six trips were done at a frequency of twice a month. The second six were done at a frequency of about once a month. In the first six sampling trips, forty-five sites were sampled during each trip. Thirty sites were sampled during each of the second six trips. Sampling included light measurements using three 4-t submersible Licor sensors with the data stored in Licor dataloggers. It also included in situ water quality sampling using Hydrolab datasondes as well as bottle samples which are analyzed in the laboratory. Laboratory bottle samples were collected using a modified Niskin bottle (Sheng and Melanson, 1999) And transported within 24 hours to the laboratory for analysis.
Light data and water quality sampling were always done at the same time. Vertical positions of the water quality sampling were consistently at 20% and 80% of the total depth, while those for the light measurements varied between sampling trips. For the first trip, measurements were taken simultaneously just below the surface and at 20% of total depth, then simultaneously at just below the surface and 50% of total depth, and then simultaneously at just below the surface and at 80% of total depth. Three replicates of each were taken about a minute apart. For trips two through five, all three Licor sensors were




23
deployed at once. One at 20% of total depth, one at 50% of total depth, and one at 80% of total depth. Again, at least three replicates were taken when possible. For the final seven trips, light measurements were taken simultaneously atjust below the surface, at 50% of total depth, and at 80% of total depth. Once again, three replicates were done with a minute between each, when possible.
Table 2.3 shows the sampling date for each and every UF sampling trip. Table 2.4 contains the sampling information for relevant light attenuation model variables. Table 2.5

Table 2.3: UF synoptic sampling trips were carried out on these dates. Trip Number Date of Trip Julian Date
1 April 8, 1997 98
2 April 25, 1997 115
3 May 6, 1997 126
4 May 20, 1997 140
5 June 9, 1997 160
6 June 25, 1997 176
7 November 20, 1997 324
8 January 29, 1998 29
9 February 26, 1998 57
10 March 26, 1998 85
11 April 30, 1998 120
12 May 28, 1998 148

Table 2.4: UF water quality variables used in the light attenuation model. Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Chlorophyll a Niskin Bottle mg/rn3 chl_a




Table 2.5: Sample sites used during UF synoptic sampling trips. Site Number Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Trips 7-12 Trips 1-6
1 1 270 55' 54" 80o 31' 21" 3089768 546981
2 3 270 58' 51" 800 32' 12" 3095209 545566
3 6 280 02' 48" 80034' 27" 3102488 541852
4 9 28007' 27" 80036' 33" 3111062 538385
5 11 280 10'21" 80038' 12" 3116408 535668
6 14 280 14' 21" 80040' 03" 3123785 532621
7 15 280 15' 45" 80040' 42" 3126367 531551
8 13 280 12' 51" 80039' 21" 3121037 533773
9 8 28006' 00" 800 35' 54" 3108388 539458
10 2 27o57' 27" 80031' 36" 3092628 546560
11 16 2817'09" 80o4127' 3128949 530318
12 19 28o21'39' 80o43' 22" 3137250 527161
13 22 28026'21'' 80044' 51" 3145923 524709
14 24 28029' 06" 80045' 48" 3150997 523165
15 28 28032' 36" 80o46' 18" 3157458 522337
16 31 28034' 30" 80o45'391' 3160876 523390
17 30 28034' 12" 80o46'54'' 3160411 521354
18 29 28032' 51" 80o44'30' 3157926 525271
19 21 28024'43' 80044' 26" 3142915 525402
20 17 280 18' 25" 80042' 00" 3131310 529414
21 42 28045' 21" 80049' 33" 3180992 517004
22 44 28044'03' 80047' 33" 3178597 520262
23 40 28043' 18" 80048' 51" 3177208 518149
24 39 28o41'57' 80047' 15" 3174720 520758
25 37 2840'09" 80048' 36" 3171392 518565
26 35 28037' 24" 80o48' 00" 3166316 519551
27 33 280 35' 48" 80o47'57'' 3163362 519637
28 36 28038' 39" 80048' 27" 3168624 518814
29 38 2841' 09" 80o48'48' 3173239 518237
30 45 28043' 37" 80045'49'' 3180992 517004




Table 2.6: Additional sampling sites used during UF sampling trips 1-6
Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
4 280 00' 18" 800 32' 45" 3097883 544655
5 280 01' 24" 800 33' 36" 3099909 543255
7 28004' 30" 80035' 09' 3105624 540696
10 28008' 51" 8037'21'' 3113643 537068
12 280 11' 39" 80038' 36" 3118807 535007
18 280 19' 57" 80o42' 36" 3134133 528427
20 28023' 21" 80043' 54" 3140387 526273
23 28o27' 48" 80045' 06" 3148600 524313
25 28029' 21" 80o44' 39' 3151463 525041
26 28030' 45" 80o46' 24" 3154043 522181
27 28031' 00" 80o45' 36" 3154507 523485

2.2.3 WQMN Data
Data was also obtained from the Water Quality Monitoring Network (WQMN). The WQMN, coordinated by SJRWMD, involved sampling monthly at thirty-four sites throughout the lagoon. Each sampling run collects between two and six samples at each location over a three day period. Care is taken in the light modeling to use light and water quality data which were taken at the same time on the same day at the same site.
Data used for this analysis were taken between March 1996 and May 1999. For reasons discussed later, these data are split into two data sets. The first data set includes 1996 -1998, while the second data set contains data collected in 1999. The locations for the WQMN sample sites are shown in Table 2.7
2.2.4 HBOI Data
Hanisak at Harbor Branch Oceanographic Institute sampled at seven sites throughout the IRL between 1994 and 1995. PAR measurements were made every 15 minutes using both 2't and 4t Licor sensors. The sensors were deployed at the top and middle of the seagrass canopies at the sampling sites. Water quality measurements were made weekly.




Care was taken to use only corresponding light and water quality measurements for model calibration. A detailed account of HBOI sampling procedures is available in their Florida Department of Environmental Protection (FDEP) Quality Assurance and Quality Control

Table 2.7: Sites sampled during WQIN sampling trips.
Sample Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Site
B02 28026'01 80038'22" 3145321 535330
B04 28022'00' 800 38'00" 3137907 535951
B06 28017'00' 80038'00" 3128675 535979
B09 28011'56' 80037'32" 3119323 536771
CCU 28004'39' 8036'08" 3105884 539105
EGU 280 07'25" 800 37'50" 3110983 536305
GUS 270 28'05" 800 32'41" 3093780 544800
HUS 28009'55" 80038'31' 3115595 535173
102 28044'20" 80048'02' 3179103 519496
107 28036'12' 80o47'54" 3164086 519739
110 280 30'04" 80046'08' 3152768 522639
113 28023'34" 80044'10' 3140773 525873
116 280 16'40" 80040'36" 3128048 531731
118 28011'40" 80038'56" 3118824 534482
121 28007'30" 80037'00" 3111141 537669
123 280 04'12" 80035'40' 3105056 539871
127 27o56'44" 80031'46' 3091293 546312
IRJO1 27047'48" 80026'56' 3074834 554311
IRJO4 27041'33" 800 23' 14" 3063324 560443
IRJO5 27039'28" 800 22'32" 3059484 561613
IRJO7 27037'11" 800 22'04' 3055272 562401
IRJ1O 27041'57" 80023'39' 3064059 559754
IRJ12 27036'34" 800 22'01" 3054134 562489
ML02 28043'35' 80043'05" 3177735 527556
SUS 270 51'15" 80029'29" 3081185 550098
TBC 28049'14" 80051'41" 3188142 513546
TUS 280 01'58" 80034'48' 3100937 541305
V05 29o00'29" 80054'34" 3208910 508841
Vil 28057'09" 80050'41 3202762 515153
V17 28052'41'' 80050'22" 3194515 515678
VMC 270 38'57" 80024'08" 3058517 558987
VSC 270 36'17" 800 22'58" 3053603 560930




27
(QAQC) manual. The HBOI sample information is shown in Table 2.8 and the sample sites are shown in Table 2.9.
Table 2.8: HBOI water quality variables used in the light attenuation model. Variable Collection Method Units Symbol
Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle Pig/L chl_a
Table 2.9: Sample sites used during the HBOI study. Site Name Site Latitude N Longitude W Easting Northing
Symbol UTM (m) UTM (m)
Banana BR 280 30' 21" 800 35'20" 540242 3153359
River
Melbourne MB 290 09' 01" 80038' 07" 535489 3224728
Turkey TC 28001'52" 800 34'35" 541655 3082043
Creek
Sebastian SN 270 51' 42" 800 29' 31" 550036 3082043
North
Sebastian SS 270 51' 00" 800 29' 18" 550392 3080734
South
Vero Beach VB 270 34' 51" 800 21' 50" 562791 3050990
Link Port LP 270 32' 10" 800 21'00" 564182 3046047

2.2.5 Phlips Data
Phlips sampled twenty-four sites throughout the lagoon during three sampling trips in July, October, and November of 1999. Light sampling was done using a Licor PAR




quantum sensor. Only data collected during the October trip are used in this analysis since only samples taken during this trip included TSS for use in the light attenuation model.
2.3 Data Set Statistics
The following are the statistics for each of the data sets used in this study. The maximum and minimum values as well as means and standard deviations are given for the model attributes of each data set.
2.3.1 SERC Data Set
Table 2.10 shows the statistics for Gallegos's SERC data set. This is the data set used by Gallegos for calibration of his light attenuation model in the southern partof the IRL. The higher color numbers are associated with the outflow from Taylor Creek, which contains outflow from Canal Structure 25. The color in this area was sometimes seen as a lens of color in the upper half meter of the water column (Gallegos, 1993).
Table 2.10: Data set statistics for the data collected during the SERC study. Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) 1.40 6.40 3.00 1.18
TSS (mg/L) < 5.00 28.60 10.71 4.94
Chlorophyll a ([tg/L) 1.11 30.77 6.18 6.27
Color (Pt Units) < 7.00 94.00 26.34 25.59
KA(PAR) (m1) 0.55 2.47 1.27 0.46




2.3.2 JF Data Sets
The UF data are divided into two data sets. The first includes data collected during synoptic sampling trips 1-6, while the second includes data collected during synoptic sampling trips 7-12. This division of data sets is for a few reasons. The first six synoptic trips took place over a three month span in the spring of 1997. The second six synoptic tripstook place over a seven month span beginning in November, 1997. As explained earlier, the light sampling techniques varied during the first six trips, but were all uniform during the second six. One lab was used for sample analysis during the first six sampling trips, but a different lab was used during the second six trips. For these reasons, it is logical to divide all of the UF data into these two data sets. The statistics for each of these data sets are given in Tables 2.11 and 2.12.
Table 2.11: Statistics for the data collected during UP synoptic sampling
trips 1-6. _ _ _
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L-) < 5.00 55.00 7.88 6.50
Chlorophyll a ([tg/L) < 1.00 20.30 5.26 2.84
Color (Pt Units) < 7.00 26.00 14.72 3.21
Kd(PAR) (m') 0.05 4.62 1.02 0.641

The greatest differences between these two data sets are in TSS and color values. In both instances, the data from trips seven through twelve have higher maximums and means. The interesting point to be made here is that even though both the color and the TSS mean




30
values are higher during the second six trips, the mean Kd(PAR) value is about the same. This will be discussed more later.
Table 2.12: Statistics for the data collected during UF synoptic sampling trips 7-12 without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 9.24 120.50 30.58 16.34
Chlorophyll a ( tg/L) 1.38 31.80 7.22 4.81
Color (Pt Units) 10.00 90.00 22.46 14.00
Kd(PAR) (m1) 0.33 2.97 0.97 0.45

2.3.3 WQMN Data Set
As described earlier, this study uses data collected by the Water Quality Monitoring Network between 1996 and 1999. This data set has been broken into two separate data sets for the purpose of analyzing the data for the light attenuation model. The first data set contains data from 1996-1998. The second contains data from 1999. This split is done to try and account for much higher TSS values found in the 1999 data.
Tables 2.13 and 2.14 show the large difference between the mean TSS values in the two data sets. The means for both chlorophyll a and color are comparable. The mean value for Kd(PAR) during 1999 is only slightly higher than that for 1996-1998, although the mean TSS is much higher. The mean values of turbidity are comparable. HigherTSS value should lead to higher turbidity values if the sampling is being done at the same locations with the same sediment types. This issue of high TSS will also be addressed later.




Table 2.13: Data set statistics for data collected by WQMN from March 1996 through 1998.
Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) < 1.00 77.40 5.23 5.25
TSS (mg/L) < 5.00 157.33 13.28 14.02
Chlorophyll a (jig/L) < 1.00 49.68 7.58 6.49
Color (Pt Units) < 7.00 85.00 24.23 12.12
Kd(PAR) (m') 0.24 3.99 1.07 0.53

Table 2.14: Data set statistics for data collected by WQMN between March and May 1999 without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
Turbidity (NTU) < 1.00 43.00 7.74 5.10
TSS (mg/L) 13.60 135.00 62.96 26.46
Chlorophyll a (pg/L) 1.34 14.87 5.88 3.04
Color (Pt Units) 10.00 52.00 21.83 8.40
Kd(PAR) (m1) 0.43 2.49 1.28 0.55
2.3.4 HBOI Data Sets
The Harbor Branch data is split into two data sets for a couple of reasons. The first is that when we received the data, we received one year at one time and then the second year at another time. Since both years had a large amount of data, it was decided to keep them separate. The other reason is that the time of day when the light sample was taken is an important input for the numerical light attenuation model. Time of day was not received




32
for the first year's data. Because of this, the first year's data are not able to be used in the numerical model. By keeping the two year's data separate, the second year's data are able to be used in the numerical model and thus for comparison with the regression model results and with numerical model results of other data sets. The first year's data are still used for the regression model. The statistics for the two years of HBOI data are shown in Tables 2.15 and 2.16.
Table 2.15: Data set statistics for HBOI data collected during HBOI's first sampling year without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 199.99 57.00 26.86
Chlorophyll a (pig[L) < 1.00 96.22 13.15 12.67
Color (Pt Units) < 7.00 128.20 17.63 18.82
Kd(PAR) (m-') 0.04 6.88 1.67 1.31

Table 2.16: Data set statistics for HBOI data collected during HBOI's second sampling year without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 24.01 159.30 67.42 24.02
Chlorophyll a (Vig[L) 3.29 79.09 16.54 12.04
Color (Pt Units) < 7.00 165.60 19.31 19.66
Kd(PAR) (inl) 0.09 6.59 1.76 1.07

Notice that for each year of sampling by Harbor Branch, the mean values for each of the variables are similar. Other than for WQMN 1999, the mean TSS values for both years




33
are higher than for the other data sets shown so far. The mean Kd(PAR) values for each year are also much higher than they are for the other data sets, including WQMN 1999.
2.3.5 Phlips Data Set
The Phlips data set is by far the smallest of the data sets used with only nineteen data records. This is because only one day of sampling included TSS sampling. The statistics for this data are shown in Table 2.17.
Table 2.17: Data set statistics for data collected by Phlips during their October 1999 sampling trip in which TSS data were collected. Variable Minimum Maximum Mean a
TSS (mg/L) 5.40 24.50 14.72 5.59
Chlorophyll a (pig/L) 8.50 28.00 18.49 5.05
Color (Pt Units) 14.00 28.00 20.05 4.21
Kd(PAR) (m"') 0.77 3.63 1.57 0.64

2.3.6 All Data Sets Comparison
The previous section shows that there are great differences between the mean values of the variables in different data sets. Not only do the mean values of a variable vary between data sets taken by different groups, but they also vary between data sets taken bythe same group. Table 2.18 shows the mean values for each variable in each data set for easy comparison.
UF Trips 7-12 have mean Kd(PAR) values which are in line with the other data sets, with UF Trips 7-12 having the lowest mean Kd(PAR) value of all of the data sets. As for the mean color values, UF Trips 1-6 has the lowest mean value of 14.72 Pt. Units, while SERC




Table 2.18: Mean values of variables of interest from each of the data sets used in this study without transformed TSS data.
Data Set Chlorophyll a Color TSS Kd(PAR)
([tg/L) (Pt Units) (mg/L) (m-1)
SERC 6.18 26.34 10.71 1.27
HBOI 1994 13.15 17.63 57.00 1.67
HBOI 1995 16.54 19.31 67.42 1.76
UF Trips 1-6 5.26 14.72 7.88 1.02
UF Trips 7-12 7.22 22.46 30.58 0.97
WQMN 7.58 24.23 13.28 1.07
1996-1998
WQMN 1999 5.88 21.83 62.96 1.28
Phlips 18.49 20.05 14.72 1.57

has the highest mean value of 26.34 Pt. Units. All of the mean values for the other data sets fall within this relatively narrow range. The chlorophyll a data also fall within a relatively narrow range between 5.26 pagJL for UF Trips 1-6 and 18.49 Vig/L for the Phlips data set.
Since we are trying to find relationships that can be used to create a model for Kd(PAR), some of these mean values do not make sense, such as all of the mean values for UF Trips 1-6 being lower than the mean values for UF Trips 7-12, except for Kd(PAR). With this being the case, we need to try to analyze the data sets more to see if these trends are seen not only for the whole data set, but also for individual samples.
2.4 The Relative Importance of Various Factors for Light Attenuation
As stated earlier, this modeling effort concentrated on predicting K/(PAR) using the important, measurable, water quality parameters of TSS, color, and chlorophyll a




35
concentration. Since the mean values for each of these variables vary between the different data sets, an analysis was done in order to find the relative contributions of these variables to the Kd(PAR).
2.4.1 Equations Used to Calculate K/PAR) Attributable to Each Variable
Using an analysis employed by McPherson and Miller (1994) in Tampa Bay and Charlotte Harbor, Florida, and by Phlips et al. (1995) in Florida Bay, the contributions to K/(PAR) are found for chlorophyll a, color, nonchlorophyll suspended solids (tripton), and water. This is shown in Equation 2.1:
Kd( PAR) = K + Kchla +Kcot + Ktrip (2.1)
where K, is the contribution to K/(PAR) due to water, Kchla is the contribution due to chlorophyll a, Kcol is the contribution due to color, and Ktrip is the contribution due to tripton. K, is taken to be 0.0384 m-' (Lorenzen, 1972), Kchla is calculated by multiplying the chlorophyll a concentration by 0.016 m2 g-1 (Phlips, personal communication), and Kco, is calculated by multiplying color by 0.014 ptr' m' (McPherson and Miller, 1987). There is not a coefficient for use in finding Krip, therefore it is found by subtracting the other K/d(PAR) components from the measured K/d(PAR) as in Equation 2.2.
Ktrip = Kd(PAR) Kw KchIla- Kco (2.2)
Because Krip must be backed out for this analysis, this is not a method that can be used to model K/d(PAR). Also note that tripton is used in this analysis, but it is not included in any of the data sets. The TSS values included in the data sets include tripton as well as




36
chlorophyll suspended solids. Tripton can be calculated by subtracting chlorophyll a concentrations corrected for pheophytin from TSS concentrations. Since TSS concentrations are usually much higher than chlorophyll a concentrations', tripton concentrations are close to that of TSS.
Equation 2.1 is able to be used since the attenuation coefficient can be partitioned into partial attenuation coefficients corresponding to different components of the water body (Kirk, 1983). Kirk did warn, though, and it should be noted that the nature of each of the attenuation coefficient contributions can be different between the components. Also, he warned that Kd(PAR), and thus the contributions to it by each component are not linear (Kirk, 1983).
2.4.2 Data Set Analysis
After values were found for Khl,,, Ko1, and Krip, each value was divided by Kd(PAR) and then multiplied by one hundred in order to find the percent contribution to Kd(PAR). Table 2.19 shows the average percentages of Kd(PAR) due to each component for each data set.
Except for WQMN 1996-1998 and UF trips 7-12, the other data sets all have tripton accounting for more than 60% of the light attenuation coefficient. Chlorophyll a accounts for between 7.80% of Kd(PAR)for the SERC data set and 16.35% of Kd(PAR) for the HBOI Year 2 data set. Color is responsible for between 17.02% of Kd(PAR) for the HBOI Year 2 data set and 33.63% of Kd(PAR) for the WQMVN 1996-1998 data set.

1 See Table 2.18, remember that TSS has units of mg/L and Chlorophyll a has units of ptg/L.




Table 2.19: Percent of Kd(PAR) due to each attenuator in this study. Data Set Average %Kd(PAR) Average % Kd(PAR) Average % KA(PAR)
Due to Color Due to Chlorophyll a Due to Tripton WQMN 33.63 11.27 50.84
1996-1998
WQMN 1999 26.22 8.00 62.17
UF Trips 1-6 25.62 9.56 60.10
UF Trips 7-12 32.84 12.69 49.94
HBOI Year 2 17.02 16.35 63.68
SERC 25.07 7.80 63.74
All Sets 24.04 13.03 59.14

Therefore, for each of the data sets, tripton contributes the most to light attenuation. The Phlips data set was not used because it is too small.
2.4.3 Percentage of Each Measured K(PAR) Due to Each Variable
Figures 2.1 through 2.3 show how the percent of the light attenuation coefficient due to color, chlorophyll a, and tripton, respectively, varies over the range of measured K/PAR) values. Each point on the graph represents the percentage for data measured along with the K/PAR) value. Notice that color and chlorophyll a both contribute a greater percentage to the light attenuation coefficient at lower measured values of K/(PAR) than they do at higher measured values of K/(PAR), where tripton clearly contributes a higher percentage.
Because of this discrepancy between different K/(PAR) values, further analysis was done to see what the relative contribution of each component is to the higher and lower measured Kd(PAR) values. The average values for the percentage of K/(PAR) due




100
a WQMN 1996-1998 S90
I o WQMN 1999
.,M 80 0
O80 UF 2-6
O 70 x UF 7-12
o70
60 0 u a ou SERC
v80
000 o HBOI Year 2
050- 0
50
S40 go n
0
20 0o
o 1 0 -,, o o 0 o
0 1 2 3 4 5 6 7
Kd(PAR) (m1)
Figure 2.1: Percentage of Kd(PAR) due to chlorophyll a.
120
0 WOMN 1996-1998 O o WQMN 1999
100 0
0O x [] a UF 2-6
xa x x x UF 7-12
080 oa x S0 00 0 SERC
"s 0 x [ axo o HBOI Year 2
60 x 1 1
0 1 2 3 4 5 6 7
ObevKd(PAR) ( n1)
40 -x2Lo)x ao oo o
20 0 [] o
oo xo o oo on o oo o o
0 1 2 3 4 5 6 7
Observed Kd(PAR) (m" )

Figure 2.2: Percentage of Kd(PAR) due to color.




120
120 .. ...... O......... ...... a W QMN 1996-1998
C100 o WOMN 1999
0 3
80 o oo UF2-6
0 Ix UF 7-12
- 60
o'o oo ox SERC
~*0 0 3 -" z
- 40 oI aO. HBOI Year 2
x xx o aX
20 o
00
I-40 0 .
go
, 1 2 3 4 5; 7
CL -20 x
-40 o
-40
Kd(PAR) (m1)
Figure 2.3: Percentage of Kd(PAR) due to tripton.
to color, chlorophyll a, and tripton for each data set above and below K(PAR) equal to 1.00 m as well as above and below the average KIPAR) for each data set are shown in Tables
2.20 and 2.21.
K(PAR) equal to 1.00 m' is chosen as a cutoff here because examination of Figures 2.1 and 2.2 show curves in the plots around this point. Another reason is because this is about the point where, in some cases, the numerical model (described in Chapters 4 and 5) goes from over predicting K(PAR) to under predicting K(PAR). The mean K/(PAR) value for each data set is chosen as a cutoff in order to see if there is a difference in data for the upper and lower K/(PAR) values of the data set. Tables 2.20 and 2.21 show that for higher K/(PAR) values, the average percentage of K/PAR) due to tripton is higher than for the lower K/(PAR) values. The exception is the SERC data set. This is because of the high color values during some of the SERC sampling. For color and chlorophyll a, the average




Table 2.20: Percentage of K/(PAR) due to color, chlorophyll a, and tripton for each data set for K(PAR) values above and below
1.00 m1.
Data Set % K/PAR) Due to Color % K/(PAR) Due to Chl_a % K(PAR) Due to Tripton
K/d(PAR) 1 K/PAR) > 1 Kd(PAR) < 1 K(PAR) > 1 K/(PAR) 1 K/d(PAR) > 1 WQMN 1996-1998 38.11 28.18 11.54 10.95 44.89 58.09
WQMN 1999 35.82 20.01 9.54 7.00 49.41 70.42
UF Trips 1-6 30.14 14.65 10.79 7.12 53.50 75.40
UF Trips 7-12 33.67 30.97 13.98 9.74 47.05 56.50
HBOI Year 1 20.30 14.12 17.57 12.43 55.99 71.33
HBOI Year2 24.35 15.37 22.00 15.08 47.18 67.41
SERC 14.35 31.06 6.47 8.54 74.57 57.68
All Sets 30.76 19.00 13.67 12.56 49.92 66.06




Table 2.21: Percentage of K/d(PAR) due to color, chlorophyll a, and tripton for each data set for K/PAR) values above and below the mean Kd(PAR) value for each data set.
Data Set Mean Avg % K/(PAR) Due to Color Avg % K/(PAR) Due to Chl_a Avg % K/(PAR) Due to K(PAR) Tripton
K/PAR) Kd(PAR) K(PAR) K(PAR) Kd(PAR) K/d(PAR)
< Mean > Mean < Mean > Mean < Mean > Mean
WQMN 1.07 37.61 27.59 11.59 10.79 45.50 58.97
1996-1998
WQMN 1.28 32.50 16.53 10.08 4.78 52.84 76.58
1999
UF 1-6 1.02 30.06 14.40 10.77 7.06 53.63 75.75
UF 7-12 0.97 33.80 30.90 14.18 9.63 46.68 56.61
HBOI
Yea 1.67 17.84 13.70 15.89 11.35 61.53 73.54
Year 1
HBOI
Yea 1.76 18.63 14.86 18.47 13.51 58.92 70.08
Year 2
SERC 1.27 17.93 35.14 6.71 9.33 71.22 53.18
All Sets 1.31 28.64 17.05 13.43 12.44 52.95 68.54




42
percentage of Kd(PAR) due to each of those is generally higher for the low Kd(PAR) values than for the higher K/(PAR) values. Of course, the exception again is the SERC data set. A portion of the SERC data set was collected near Taylor Creek, which contains outflow from a canal structure. Data from the Taylor Creek area show higher color data including an occasional lens with high color values on the surface of the water.
In previous studies using this analysis, tripton also accounted for the largest relative percentage of K/(PAR), but color and chlorophyll a varied. Phlips et al. (1995) studied seventeen sites sampled during 1993 and 1994 in Florida Bay, Florida. The average percentages for all of the sites together show tripton accounted for approximately 74.28% of Kd(PAR), while the chlorophyll containing particles accounted for approximately 14.24% of K/(PAR), and apparent color 7.35%. McPherson and Miller (1987), using samples colleted in Charlotte Harbor, Florida during 1984 and 1985 found on average that tripton accounted for 72% of the total K/(PAR), color accounted for 21%, and suspended chlorophyll accounted for approximately 4%.
2.4.4 Analysis by Section
The same analysis performed on each of the data sets was also done for each of the five sections of the IRL used in this study. The five divisions are a South section below Northing UTM 3111063 m near Eau Gallie River, a Middle section between Northing UTM 3111063 m and Northing UTM 3154507 m just south of where state road 405 crosses the IRL a North section above Northing UTM 3154507 m, Banana River, and Mosquito Lagoon. The divisions were made to try to group sample sites according to like sections of the lagoon and also to have enough data for analysis in each section. As seen in Table 2.22,




43
the results are very similar for each of the sections with tripton contributing the most to the light attenuation coefficient, followed by color and the chlorophyll a.
Table 2.22: Percent of Kd(PAR) due to color, chlorophyll a, and tripton for each section of the IRL.
Section % Kd(PAR) Due to % Kd(PAR) Due to % Kd(PAR) Due to
Color Chla Tripton
North 25.08 12.12 58.54
Middle 27.80 12.16 55.67
South 24.17 12.63 60.04
Banana 22.18 14.85 57.92
River
Mosquito 28.09 10.53 57.48
Lagoon
2.4.5 Analysis by Season
The same analysis was also done for each season in order to see if different components had different influences at different times of year. The results are shown in Table 2.23. Again, not much variation is seen between the different seasons. Two things that are noticed, though, are that the average percentage of Kd(PAR) due to color goes down as the year goes on and the average percentage of Kd(PAR) due to chlorophyll a increases from the first half of the year to the second half of the year. Data from 1998 show an increase in chlorophyll a during the fall (Chenxia Qiu, personal communication). In each season, tripton again contributes the most to the total light attenuation, followed by color and chlorophyll a.




Table 2.23: Percent of K/PAR) due to color, chlorophyll a, and tripton for each season. Season % Kd(PAR) Due to % K/(PAR) Due to % K/(PAR) Due to
Color Chla Tripton
Jan. March 27.14 11.23 57.99
April June 25.10 11.04 59.39
July Sept. 24.35 15.27 56.89
Oct. Dec. 22.45 15.60 58.74

While the preceding analyses show relative contribution of each component to the total Kd(PAR) for each data set, it must be remembered that they are approximations. It must also be remembered that the values for tripton are calculated by subtracting the contributions to Kd(PAR) from the other variables from the total K/(PAR) from data. This, therefore, does not come from the actual tripton data. Since tripton is closely related to TSS, these Krip may not follow along well with TSS data either. An example of this may be seen by examining the two different UF data sets. While the first six UF sampling trips have a mean TSS value of 7.88 mg/L and the second six sampling trips have a mean TSS value of 30.58 mg/L, the percentages of K/(PAR)due to tripton in each data set are 60.10% and 49.94%, respectively. This may show a little of two things. The first is that the mean color value for the second six sampling trips is higher (22.46 Pt. Units, as opposed to 14.72 Pt. Units for the first six trips) and therefore, using this method of analysis, leaves less K/PAR) to be associated with tripton. While this may indicate a flaw in this analysis, it also goes against intuition. The average chlorophyll a values for the two data sets are 5.26 Vg/L for the first six sampling trips and 7.22 [ig/L for the second six sampling trips. These are very similar with the average for the second six trips being slightly higher. Intuition would say that if the amounts of each




45
of the attenuators increase, so should the attenuation, but in this case the average light attenuation coefficient for the first six trips is 1.02 m', while for the second six trips the light attenuation coefficient is 0.97 m-.
2.5 Data Differences
Differences in data sets are inevitable, even when every precaution is taken to minimize them. Each data set is being collected by different people who may have all been taught the same exact techniques, but each may do things in slightly different ways when confronted with the challenges of sampling in the field. Compounding the problem for this task is not only different people in one group collected data, but different groups collected data and different labs analyzed the data. Analysis of the processed data for each set showed differences in the data, particularly total suspended solids (TSS). Some of the most obvious differences occurred between UF synoptic trips 1-6 and UF synoptic trips 7-12, as well as between WQMN data sampled before and after March, 1999. The two years of HBOI sampling also showed higher TSS values, but do not have a source for comparison as the UF and WQMN data do. Since our goal was to use as much of the available data as possible, ways were sought to adjust for these differences.
Since the IRL is a shallow estuary, resuspended sediment would be expected to increase during wind events (Sheng et al., 1992). Suspended sediment would also be expected to be a main cause of light attenuation (McPherson and Miller, 1987; Phlips et al., 1994). Therefore, Ka(PAR) would be expected to show a positive correlation with TSS. Accordingly, higher TSS values would be expected to correspond with higher K/(PAR) values. This was not found to be the case when comparing different data sets, particularly when comparing WQMN data collected between 1996-1998 to WQMN data collected in




46
1999, and also UF data collected in the first six synoptic trips to UF data collected during the second six synoptic trips. While WQMN 1999 data and UF trips 7-12 data contained much higher TSS numbers than the previous sampling by each group had shown, the average Kd(PAR) values were not appreciably higher, which runs counter to expectations.
2.5.1 UP Data
As stated in the previous section, the average K/(PAR) value for UF's second six sampling trips is less than that for the first six sampling trips, despite a higher average TSS value. The regressions for Kd(PAR) against TSS for the UF sampling trips 7-12, while very poor with R2=0.00 13, does show a negative relationship for Kd(PAR) against TSS, as shown in Equation 2.3.
Kd (PAR) = -0.001 TSS + 0.9968 (R2 = 0.0013) (2.3)
UF sampling trips 1-6 show a positive correlation between K/(PAR) and TSS as seen in Equation 2.4.
Kd(PAR) = 0.0619 TSS + 0.5309 (R2 = 0.40) (2.4)
The graphs of K/(PAR) against TSS for both of these data sets are seen in Figures 2.4 and 2.5. To better illustrate the differences between the two data sets, the average TSS value for UF sampling trips 7-12 (TSS = 30.58 mg/L) is used in the regression for K/(PAR) from UF sampling trips 1-6. The result is a predicted K/PAR) of 2.42 m-', while the average K/(PAR) for the second six sampling trips is only 0.97 m"1. The result of using the UF 7-12 average TSS value in the equation for sampling trips 7-12 is the same Kd(PAR) as the average of 0.97 m'. This illustrates that if the regression relationship for sampling trips 1-6 is




47
correct, then the K/(PAR) values for sampling trips 7-12 should be higher according to the corresponding TSS values.
2.5.2 WQMN Data
The same discrepancies between TSS K(PAR) equations are seen in the WQMN data sets, even though the R2 values for the regressions are not as high. While the regression for K/(PAR) against TSS for WQMIN 1999 does not have a negative correlation, it does have a much gentler slope than the regression for WQMN 1996-1998. This is seen in Figures 2.4 and 2.5, where the regression equation for WQMIN 1996-1998 is:
Kd (PAR) = 0.0282 TSS + 0.7299 (R2 = 0.22) (2.5)
5.00 --- ------- ----4.50 y = 0.0619x + 0.5309
R2= 0.3994
4.00
.00
2.50
0.50
0.00 .. .
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
TSS (mg/I)
Figure 2.4: UF sampling trips 1-6 relationship between Kd(PAR) and TSS.




5.00 4.50 4.00 '3.50 D.,3.00
M 2.50 M 2.00 1.50
1.00 0.50

y = -0.001x + 0.9968
R2= 0.0013
* *
'.. i" -. = "" ". ,I

U.UUJ I I I II
0.00 20.00 40.00 60.00 80.00 100.00
TSS (mg/I)
Figure 2.5: UF sampling trips 7-12 relationship between Kd(PAR) and TSS.
and the regression equation for WQMN 1999 is :
Kd (PAR) = 0.0053 + 0.9472 (R2 = 0.0529) (2.6)
If the average TSS value for WQMN 1999 (TSS = 62.96 mg/L) is used in the WQMN 1996-1998 equation, it predicts a K(PAR) of 2.51 m-1, compared to an average K(PAR) for WQMN 1999 data of 1.28 m-'. If the average WQMN 1999 TSS value is used in the WQMN 1999 equation, it predicts the average KIPAR) of 1.28 m.
The Turbidity and TSS relationships should also be examined here to see if they match up well for the WQMN data sets. Figures 2.8 and 2.9 show the relationships for WQMN 1996-1998 and WQMN 1999, respectively. The regression equation for WQMN 1996-1998 is:
Turbidity = 0.3427 TSS + 1.0217 (R2 = 0.6769) (2.7)

while the regression equation for WQMN 1999 is:




Turbidity = 0.1148 TSS + 2.0551 (R2 = 0.3442). (2.8)
As for the TSS relationships with K(PAR), there are differences between the Turbidity TSS relationships of each data set. The slope for the WQMN 1999 regression is about a third of what it is for the WQMN 1996-1998 data set. This means that as the TSS values increase, the 1996-1998 data indicate a much higher turbidity than the 1999 data indicate. So, if a TSS value of 50 mg/L is used in both of those equations, the 1996-1998 equation predicts a turbidity value of 18.16 NTU's, while the 1999 equation predicts a turbidity value of 7.80 NTU's. Turbidity was not measured during the UF sampling trips so this type of comparison can not be done for those data sets.

5.00
y = 0.028
4.50
4.00
U
S3.503.00
S2.50
< 15 ";--,2.00 .
1 50
1.0o i-m r M E
0.50 4 N
0.00 .
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
TSS (mg/I)
Figure 2.6: WQMN 1996-1998 relationship between Kd(PAR) and TSS.

90.00 100.00




5.00 4.50 4.00
-'*3.50 E3.00 CC 2.50 n 2.00 2 1.50
1.00 0.50 0.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 TSS (mg/L)
Figure 2.7: WQMN 1999 relationship between Kd(PAR) and TSS.

90.00 100.00

90 .00 - - --- - ---- ------
y80.00 = 0.3427x + 1.0217
0.00 R2= 0.6769
70.00
1- 60.00zU
050.00
13 40.00 -----30.00 U
2 0 0 0 A
10.00 ** 7 1
0.00 N. "r
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 TSS (mg/L)
Figure 2.8: WQMN 1996-1998 relationship between turbidity and TSS.

160.00

y = 0.0053x + 0.9472 R = 0.0529
U
U U U
U
U!
U1
i i I ii i i




90.00
80.00 y = 0.1148x + 2.0551
R= 0.3442
70.00
60.00
I
z
50.00
"0 40.00
_ 30.00
20.00 _,
10 1 1moil
20.00
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.9: WQMN 1999 relationship between turbidity and TSS.
2.5.3 HBOI Data
Both years of sampling by HBOI show relatively high average TSS values with the average TSS for HBOI Year 1 being 57.01 mg/L and the average for HBOI Year 2 being 67.43 mg/L. The average K/PAR) values are also higher than for the other data sets with the average K/(PAR) for HBOI Year 1 being 1.67 m- and the average for HBOI Year 2 being 1.76 m' To see if these numbers are consistent with any of the trends seen in the other data sets, the average TSS values for HBOI Years 1 and 2 are used in the K(PAR) TSS and Turbidity-TSS regression equations of the other data sets. The regression equations for Kd(PAR) TSS and Turbidity TSS for HBOI Year 1 are shown in Equations 2.9 and 2.10, with the graphs being shown in Figures 2.10 and 2.11.
Kd (PAR) = 0.0201* TSS + 0.5057 (R2 = 0.1806) (2.9)

Turbidity = 0.1916 TSS 4.0611 (R2 = 0.5685) (2.10)




52
The regression equations for HBOI Year 2 are shown in Equations 2.11 and 2.12. The graphs of the relationships are shown in Figures 2.12 and 2.13.
Kd (PAR) = 0.0044 TSS + 1.462 (R2 = 0.0095) (2.11)
Turbidity = 0.1151* TSS + 0.5324 (R2 = 0.2114) (2.12)
The results using average HBO1 TSS values in each of the regression equations are shown in Tables 2.24 and 2.25.
As is seen in Table 2.25, the predictions for KI(PAR) using the average TSS
values for HBOI Years 1 and 2 in the K(PAR) TSS regression equation for each data set
7 .0 0 .................. ............. ....... . ........... . .............. ..........
6.00 = 0.0201 x + 0.A0571
R2= 0.1806
-.5.00
E
4.00
1.00 .
0 O0
0.00 i i I I I i
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.10: HBOI year 1 relationship between Kd(PAR) and TSS.




5 0 .0 0 ..................... .......... ............ ... ....... ........... ..... .. ......... .................... .. ..... ...... ..... ............... ............... ..... ....... .... ... ....................... ... ........ ................... .............. ......... .
50.00 - - - -- - - --- -45.00 y = 0.1916x 4.0611 q
R = 0.5685
40.00
335.00Z 30.00 .25.00
20.00
015.00
0.0
15.00 IN
I- I
10.00 U U no ut U
5.00 I mI
0.00 ....N9
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.11: HBOI year 1 relationship between turbidity and TSS.
7.00
. y =0.0044x + 1.462
6.00-2
6.00 R2 = 0.0095
5 G.00
4.00 I
IN af IU N* I NO. I
2.00 = 1 I
% IN Ni
1.00 I-" :.-ui- ==-" =
IN ~ h .m IN IN* U
0.00 U ,
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 TSS (mg/L)
Figure 2.12: HBOI year 2 relationship between Kd(PAR) and TSS.




50.00
45.00 40.00 $35.00 Z 30.00 .>25.00
20.00 15.00
10.00
5.00 0.00

y = 1151x + 0.5324 R = 0.2114
. ,
-Ai

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)
Figure 2.13: HBOI year 2 relationship between turbidity and TSS.

Table 2.24: Turbidity calculations using HBOI years 1 and 2 average TSS values. Data Set HBOI Year 1 HBOI Year 2 WQMN 96-98 WQMN 1999
HBOI Year 1 6.86 7.09 22.56 8.60
HBOI Year 2 8.86 8.29 24.13 9.80
Table 2.25: K(PAR) calculations using HBOI years 1 and 2 average TSS values. Data Set HBOI HBOI WQMN WQMN UF 1-6 UF 7-12
Year 1 Year 2 1996-98 1999
HBOI
Yea 1.65 1.71 2.34 1.25 4.06 0.94
Year 1
HBOI
Yea 1.86 1.76 2.63 1.30 4.70 0.93
Year 2




55
vary greatly. The average K/(PAR) value for each HBOI data set is best predicted by the K/(PAR) TSS regression equation for that data set. The K/(PAR) TSS equations from the WQMN 1996-1998 and UF 1-6 data sets, the data sets with lower TSS values, overpredict the average K/PAR) for the HBOI data, while WQMN 1999 and UF 7-12, the data sets with higher TSS values, underpredict. This indicates that there are major differences between the
data sets which could cause problems when trying to model all of the data sets at once.
2.5.4 Attempt to Make TSS Data Uniform
The one similarity for both the WQMN and UF data sets is a change of labs for
sample analysis occurred between the separation of data for both sets. One lab did the analysis for WQMN 1996-1998 and the first six UF sampling trips. Another lab did the analysis for WQMN 1999 and the second six UF trips2. If it can be assumed that sampling methods and techniques used by both groups remained the same between sampling trips, then
a closer look at the labs used for sample analysis should be taken.
Split sample analysis was done in order to try and determine if there were differences
between the analyses done by the two labs. Samples were taken at the northern UF inshore sampling tower at 280 39' 18.36" N latitude and 800 48' 4.02" W longitude at 14:00 EST on 13 April 2000. The samples were taken in a Niskin type bottle at 20% and 80% of the total depth. One sample for each lab was taken out of the same Niskin bottle sampling with care being taken to assure uniformity between the samples. Two samples from the upper location
2The changing of labs occurred after UF sampling trip number 6 for the UF data. For the WQMN data the change took place in October of 1998. While the WQMN data does not show an increase through the end of 1998, the first data used in 1999 was in March. The reason the jump did not occur in WQMN data for October through December 1998 is not known.




56
and two from the lower location were each sent to each of the labs. The results are shown in Table 2.26.
Table 2.26: Results from TSS split sample analysis. _______________Laboratory Upper Level TSS Value (mg/L) Lower Level TSS Value (mg[L)
Lab 1 17.4 15.8
Lab 2 135.0 36.2

The results for the lower samples are somewhat similar, but the initial results for the upper samples are extremely different with the number from the second lab being extremely high. This was brought to the attention of the second lab and the results from the first lab were revealed. The second lab then redid their calculations and presented a corrected value of 17.8 mgfL. When asked to see what was done, we did not get a detailed account from the second lab, but instead a description of what should have been done.
Since these discrepancies did exist, any model which used TSS as an input to try to predict KI(PAR) values would not be able to be calibrated to both of these extremes (an explanation of the models will appear later). An attempt needed to be made to find a relationship between the TSS values found by both labs in order to try to convert all of the TSS data to resemble that of one lab. Since the TSS reported by the first lab had a better correlation with K/(PAR), the numerical model (which will be explained later) was calibrated using TSS numbers which resemble the first lab results, and there are more data resembling that from the first lab, it was decided to try to find a way to convert the data from the second lab to resemble that of the first.




57
The common thread which was found to do this is the turbidity measurements for the WQMN data. Turbidity data are also analyzed by the labs, but we do not have reason to suspect major differences in the methods used by the two labs. Therefore, the Turbidity TSS relationships shown in Figures 2.8 and 2.9 are used for the conversion. The TSS numbers for UF synoptic sampling trips 7-12 as well as WQMN 1999 are converted to turbidity using the Turbidity -TSS relationship for WQMN 1999 data (Eq. 2.8). These "turbidity" numbers were then used in the rearranged WQMN 1996 1998 Turbidity TSS relationship to find the converted TSS values.
(Turbidity- 1.0217)
TSS = .32 (2.13)
0.3427
Since the two HBOI data sets also contain high TSS values, the same conversion method is used in order to make the TSS data more uniform for easier use in the numerical model.
2.6 Data Sets Statistics With Converted TSS Values
This section shows the TSS statistics for the data sets with the high original TSS values after the conversion using the TSS-Turbidity relationships from WQMN 1996-1998 and WQMN 1999. It also shows the data statistics, including the converted TSS values for each season and also for the five different sections of the IRL used in this analysis.
2.6.1 Converted TSS Data Sets
The statistics for the converted TSS values are shown in Table 2.27. The other variables are not shown because they did not change. Table 2.28 shows a comparison between the original and converted TSS values for each data set. The mean TSS values for UF sampling trips 7-12, WQMN 1999, HBOI Year 1, and HBOI Year 2 decrease between




58
the original and converted TSS values by 56.64%, 61.72%, 61.21%, and 62.03%, respectively.
Table 2.27: Transformed TSS statistics using WQMN 1994-1998 and WQMN 1999 turbidity-TSS relationships;
Data Set Minimum TSS Maximum TSS Mean TSS Standard Deviation
(mg/L) (mg/L) (mg/L) (mg/L)
UF 7-12 6.11 43.38 13.26 5.47
WQMN 7.57 48.24 24.10 8.86
1999
HBOI 1 3.02 70.01 22.11 9.00
HBOI 2 11.06 56.38 25.60 8.05

2.6.2 Seasons Statistics
All of the data sets are combined for use in the data sets for each season. The seasons are divided into four three month data sets. The first division is January March,the second one is April June, the third is July September, and the fourth is October December. The statistics for each of these are shown in Tables 2.29 through 2.32.
Examining the mean values, chlorophyll a has the lowest mean concentration during April June at 6.66 Vig/L and the highest average concentration of 15.32 pig/L during October December. Color has its lowest mean value of 15.95 Pt. Units during April June and its highest mean value of 24.76 Pt. Units during October December. The lowest mean TSS concentration of 14.42 mg/L comes during April June and the highest mean TSS concentration of 18.46 mg/L comes during October December. As would be expected, April June, which has the lowest mean values of the other variables, also has the lowest




59
K/(PAR) value of 1.09 m'. Along those same lines, October December has the highest
mean values for each of the variables and also the highest mean value of Kd(PAR) of
1.60 m-'.
Table 2.28: TSS (mg/L) statistics for data transformed using WQMN 1994-1998 and WQMN 1999 turbidity-TSS relationships. Data Set MinimumTSS Maximum TSS Mean TSS Standard Deviation
UF 7-12 9.24 120.50 30.58 16.34
Original
UE7-12 6.11 43.38 13.26 5.47
Converted
WQMN
1999 13.60 135.00 62.96 26.46
Original
WQMN
1999 7.57 48.24 24.10 8.86
Converted
HBOI 1 0.01 199.99 57.00 26.86
Original
HBOI 1
Co 3.02 70.01 22.11 9.00
Converted
HBOI 2
Oi 24.01 159.30 67.42 24.02
Original
HBOI 2
Co 11.06 56.38 25.60 8.05
ConvertedII

2.6.3 Sections Statistics
The statistics for each of the sections of the IRL are presented here to see if any noticeable differences are present. This information may be important later for calibration of the numerical light attenuation model. The statistics are shown in Tables 2.33 through 2.37.




60
For the sections, Mosquito Lagoon has the highest TSS mean value with 23.65 mg/L while Banana River has the lowest mean TSS value of 13.43 mg/L. Chlorophyll a concentration is the highest in the South Section with a mean value of 12.39 jig/L and is the lowest in the Middle Section with a mean value of 7.23 Vig/L. For Color, the highest mean value occurs in the South Section with a value of 25.02 Pt. Units and the lowest mean value occurs in the Middle Section with a value of 13.43 Pt. Units. As for the K/(PAR) values, the highest mean value is 1.60 m-1 for the South Section which has the highest mean values for color and chlorophyll a. It also has the second highest mean TSS value of 19.37 mg/L. The lowest mean Kd(PAR) value is 0.94 m1 in the Banana River. The only other variable with the lowest mean value being in the Banana River is color.
Table 2.29: Statistics for January March with transformed TSS values. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 70.01 16.54 10.97
Chlorophyll a ([tg/L) 1.11 50.55 9.33 7.70
Color (Pt. Units) < 7.00 94.00 21.87 15.41
Kd(PAR) (m') 0.09 6.84 1.40 1.04




Table 2.30: Statistics for April June with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 89.50 14.42 10.81
Chlorophyll a (jig/L) < 1.00 37.22 6.66 4.98
Color (Pt. Units) < 7.00 69.90 15.95 7.93
Kd(PAR) (m') 0.05 4.62 1.09 0.65
Table 2.31: Statistics for July September with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 43.20 17.92 9.62
Chlorophyll a (pig/L) < 1.00 68.57 13.36 11.00
Color (Pt. Units) < 7.00 103.60 23.53 17.95
Kd(PAR) (m1) 0.33 6.88 1.45 0.90
Table 2.32: Statistics for October December with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 43.38 18.46 8.02
Chlorophyll a (pig/L) 1.81 96.22 15.32 13.80
Color (Pt. Units) < 7.00 165.60 24.76 22.24
Kd(PAR) (m-') 0.04 6.59 1.60 1.05




Table 2.33: Statistics for the South Section of the IRL with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 70.01 19.37 10.98
Chlorophyll a (pg[L) < 1.00 96.22 12.39 11.09
Color (Pt. Units) < 7.00 165.60 25.02 20.49
Kd(PAR) (m-') 0.04 6.88 1.60 1.01
Table 2.34: Statistics for the Middle Section of the RL with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 49.00 9.73 7.33
Chlorophyll a ([ig/L) < 1.00 35.01 7.23 4.97
Color (Pt. Units) 7.50 70.00 18.22 8.16
Kd(PAR) (m') 0.33 3.71 1.00 0.46
Table 2.35: Statistics for the North Section of the IRL with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 55.00 14.74 8.91
Chlorophyll a ([tg/L) < 1.00 68.57 8.96 8.80
Color (Pt. Units) < 7.00 90.00 16.51 9.41
Ka(PAR) (m') 0.05 6.43 1.23 0.88




Table 2.36: Statistics for the Banana River with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) < 5.00 37.90 16.56 7.39
Chlorophyll a (,ig/L) < 1.00 79.09 8.36 9.32
Color (Pt. Units) < 7.00 52.00 13.43 6.41
Kd(PAR) (m') 0.09 6.22 0.94 0.64
Table 2.37: Statistics for the Mosquito Lagoon with transformed TSS. Variable Minimum Maximum Mean Standard
Deviation
TSS (mg/L) 6.60 89.50 23.65 15.99
Chlorophyll a (jig/L) 1.58 22.90 7.95 6.14
Color (Pt. Units) 11.00 45.00 21.27 8.21
Kd(PAR) (m1) 0.43 3.16 1.28 0.66




CHAPTER 3
REGRESSION MODELS
3.1 Introduction
One way to try to find a light attenuation model is to find a simple regression relationship between the Kd(PAR) calculated from light measurements and the water quality measurements taken simultaneously. This type of empirical model is a simple way to relate light attenuation to water quality at a certain time. This method was used previously by McPherson and Miller (1994) in Tampa Bay and Charlotte Harbor.
The water quality parameters used for the regression analysis are total suspended solids (TSS), chlorophyll a (chl-a), and color. The chlorophyll a concentration is related to the phytoplankton concentration in the water while the color in the water is related to dissolved organic matter within the water. These parameters are chosen for three main reasons. The first is that they are all known light attenuators (Gallegos, 1993). The second is that they are the same parameters used in the numerical light attenuation model which is being tested. This enables an easier comparison between the models. The third reason is that they are recognized as actual light attenuators. An example of the opposite of this would be using salinity in a light attenuation model for highly colored water coming from a freshwater source. Here, salinity may be very well correlated with light attenuation, but the color in the water is what is doing the attenuating, not the salinity. McPherson and Miller (1994) found a relationship between the light attenuation coefficient and salinity to have a ? = 0.71 in




65
Tampa Bay and Charlotte Harbor, but note that the increase in attenuation comes from an increase in color, suspended matter, and nutrients causing algal growth.
Using those three parameters, the best one-variable, two-variable, and three-variable linear stepwise regression models are produced for each of the available data sets using the PROC REG option available in SAS software (SAS Institute Inc, 1990). Using the stepwise method means that just because a variable is used in the one-variable model, it does not necessarily need to be used in the two-variable model, thus allowing for the best model to be found. In addition, a three-variable, non-linear factorial regression model is also produced for each data set using the PROC GLM option in SAS software. Whereas the simple regression models have one coefficient for each variable, as well as an intercept, the factorial model also includes coefficients for products of the variables. Each model also includes an R' value to help judge the fit as well as a p value in order to measure the significance of each component in the model.
In addition to finding the models for each of the data sets separately, linear regression and factorial models have been developed for all of the available data together at once. The combined data were then divided into seasons and sections of the IRL to see if time or space dependent models would provide better results. Not enough data were available to divide each separate data set into seasons and sections. The seasonal divisions are January March, April June, July September, and October December. The sections of the lagoon used include Banana River, Mosquito Lagoon, a southern section up to Northing UTM 3111063 mn near Eau Gallie River, a middle section between Northing UTM 3111063 mn and Northing UTM 3154507 m just south of where state road 405 crosses the IRL, and a northern section north of Northing UTM 3154507 m.




3.2 Regression Model Statistics
In order to understand the analysis used in this chapter, a few terms need to be defined. The "fit" of the regression model to the data is determined using the coefficient of determination, r2. For a linear regression model using one independent variable and one dependent variable, r2 indicates the percentage of the total sums of squares that is fit by the regression model (Weimer, 1987). Weimer (1987) gives a good explanation ofjust what this means and how it is calculated.
To see if the regression model that has been calculated is dependable enough to be used for modeling the dependent variable, a hypothesis needs to be tested. The hypothesis tested is known as the null hypothesis, HO. Weimer (1987) defines the null hypothesis as the hypothesis of "no difference." The null hypothesis for this study is that the model does not predict KPAR. So for the regression equation in Equation 3.1:
5 = bo + bix (3.1)
the null hypothesis would be that b, = 0 and therefore
5 = bo(3.2). If this is the case, then each answer for y is bo, no matter what values x is, so x makes "no difference." If this is the case, then we say: Y5= bo(3.3) So then we have three different values for y: the observed value, y, the value calculated by the regression equation, 5,and the result of the null hypothesis, Y5. There is a deviation between y and 57. This can be partitioned into the difference between 5 and5,




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which is the deviation due to the regression, and the difference between y and 5 which is the deviation due to error. This is shown in equation 3.4.
y- y= (y- 9)- (-y) (3.4)
The sum of the squares of each component satisfies: (Y-_ (Y_ )2+ y -)2 (3.5)
where:
sum of squares of y (SSy) = (Y )2 (3.6)
sum of squares for error (SSE)= 2 (Y- ) (3.7)
sum of squares for regression (SSR) = (5- (3.8).
Using the above definitions, r2 is defined in:
r2 = SSR/SSy (3.9).
The r2 is used to denote the coefficient of determination since it can be shown to be the square of the Pearson correlation coefficient, r (Weimer, 1987). A Pearson correlation coefficient with a value of 0.60 is being taken here to indicate real world significance (Kornick, 1998). This correlates with a r2 of 0.36. For the cases when more than one variable is used in the regression equation, the multiple correlation coefficient R2 is used. In the case of this paper, R2 is used to denote the correlation coefficient for each regression model, therefore keeping with the same notation as the SAS output.




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An F distribution is used to determine if the model and each variable in the model are statistically significant. In order to use an F distribution, first an F statistic must be calculated. For the regression model, an F statistic is calculated with: SSR
F 2 (3.10)
Se
where SSR is defined in equation 3.8 and S2, the residual variance, is defined in:
e
S2 = SSE (3.11).
e n 2
where SSE is defined in equation 3.7 and n is the number of points.
The degrees of freedom for the numerator and denominator of Equation 3.10 are needed since the F distribution is dependent upon degrees of freedom in its constituents. By definition, the degree of freedom in the numerator is one. The degrees of freedom for the denominator are n 2. The degrees of freedom as well as the F statistic are then used to find a probability value ( p value) for the model. This p value, when compared to a level of significance (a) is used to determine if the null hypothesis can be rejected or not. Weimer (1987) defines the p value as "the smallest level of significance that would have resulted in HO being rejected." If the p value is less than a (in this case 0.05), then the null hypothesis can be rejected and the model is statistically significant.
An F statistic is also calculated for each added variable with Equation 3.12 to see if the null hypothesis can be rejected for each variable.




F- AR2/g (3.12)
In Equation 3.12, AR 2 is the change in R 2 with the addition of the new variable, g is the number of new variables added, n is the number of points, k is the total number of variables used (Wonnacott and Wonnacott, 1977). In this equation, g are the degrees of freedom in the numerator and n k 1 are the degrees of freedom in the denominator. These are used to find a p value the same way as they are for the F statistic for the entire model.
In general, the larger the F statistic is, the smaller the p value is, and therefore the chances are better of having the model or variable be statistically significant. Because of the position of the total number of samples, n, in the equations, it can be seen that larger values of n lead to larger values of F statistics. Therefore, larger data sets have a better opportunity of having the variables and regression model be statistically significant.
3.3 Regression Models for Various Data Sets
In this section the best one, two, and three variable stepwise regression models as well as the best three variable factorial model are presented for each individual data set and for the combined data set. This allows for comparison to see how compatible a model for one data set may be with another data set.
3.3.1 Best One-Variable Linear Regression Model for Each Data Set
The results for the best one variable model for each data set are shown in Table 3. 1. Many things can be seen just by looking at the results for the best one-variable model. The first, by looking at the R' values, is that the SERC data set has the best fitting one-variable model with R 2=O .6824. The best one-variable model for this data set uses color as the variable.




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This makes sense in that one of the goals of Gallegos using this data set (Gallegos, 1993) was to be able to investigate the effects of color on light attenuation modeling. Also, this data set included sampling at Turkey Creek, where a color lens was found on the surface of the water and was attempted to be modeled. All of the one-variable models for the other data sets, including the combination of all of the data, are statistically significant to the 0.05 level except WQMIN 1999 and Phlips which are very small data sets (Table 3.2). Of the data sets in which the TSS values were highest (Harbor Branch Year 1, Harbor Branch Year 2, UF Trips 7-12, and WQMN 1999) HBOI Year 2 and UF Trips 7-12 do not have TSS as the best one variable model, but instead use color and chlorophyll a, respectively. Also, even though only UF Trips 7-12 has chlorophyll a in the model, and five of the eight separate data sets have TSS, the combination of all of the data sets has a one variable model with chlorophyll a.
Table 3.1: Best one-variable regression model for each data set. Data Set Coefficient and Variable Intercept R 2
All Sets 0.04085 chla 0.90280 0.1935
HBOI Year 1 0.06132 tss 0.31317 0.1776
HBOI Year 2 0.02117 color 1.34719 0.1499
UF Trips 1-6 0.06187 tss 0.53106 0.3994
UF Trips 7-12 0.03594 chl-a 0.70714 0.1492
WQMN 1996-1998 0.02823 tss 0.72991 0.2179
WQMN 1999 0.01610 tss 0.89213 0.0662
Phlips 0.03310 tss 1.07845 0.0838
SERC 0.01479 color 0.88387 0.6824




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Perhaps the best point that can be made from these results is the variation between data sets, not only variation in the variables used for each data set's model, but also the variation between equations in which the same variable is used. This agrees with Kornick's (1998) findings. Since there is such variation in variables used, we must add another variable to see if there is an improvement.
Table 3.2: F values and p values for the best one-variable regression models. Data Set Variable F Value p Value
All Sets Chla 302.70 < 0.0001
HBOI Year I TSS 35.41 < 0.0001
HBOI Year 2 Color 52.38 < 0.0001
UF Trips 1-6 TSS 158.24 < 0.0001
UF Trips 7-12 Chla 24.02 < 0.0001
WQMN 1996-1998 TSS 88.05 < 0.0001
WQMN 1999 TSS 1.98 0.1699
Phlips TSS 1.55 0.2294
SERC Color 109.60 < 0.0001

3.3.2 Best Two-Variable Linear Regression Model for Each Data Set
By adding a second variable to the regression models, the R2 values improve for all of the data sets as shown in Table 3.3. Again, neither of the variables used in the models for the Phlips data set nor for the WQMN 1999 data set are statistically significant at the 0.05 level. This is due, at least in part, to the small sizes of each of those two data sets.
As shown in Table 3.4, another interesting note is that the two variable regression model for all of the data sets combined uses TSS and color (both of which are more statistically significant with p values of <0.0001), while chlorophyll a is used in the one




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variable model and is statistically significant at the 0.05 level in that model with a p value of <0.0001.

Table 3.3: Best two-variable model for each data set. Data Set Coefficient Coefficient Intercept R2 R2
and Variable and Variable Improvement
All Sets 0.04153 tss 0.02058 color 0.22263 0.3135 0.1200
HBOI
Year 0.077041 tss 0.03235 color -0.60507 0.3822 0.2046
Year I
HBOI 0.01822 color 0.02807 chla 0.93994 0.2459 0.0960
Year 2
UF
Ti 0.05431 tss 0.04812 chla 0.33744 0.4394 0.0400
Trips 1-6
UF
Ti 0.01135 color 0.03681 chla 0.44584 0.2753 0.1261
Trips 7-12
WQMN 0.02594 tss 0.01649 color 0.35790 0.3592 0.1413
1996-1998
WQMN 0.02081 tss 0.04235 chla 0.52962 0.1144 0.0482
1999
Phlips 0.04447 tss 0.03593 color 0.19068 0.1297 0.0459
SERC 0.01495 color 0.01715 chla 0.77365 0.7375 0.0551

Using an R2 of 0.36 to determine if the regression model has real world significance, the two variable models for HIBOI Year 1, UF Trips 1-6, and SERC all fit that criterion. In order to see if any more data sets can have models which fit this criterion, a third variable is added.
3.3.3 Best Three-Variable Linear Regression Model for Each Data Set
Table 3.5 shows the best three variable linear regression model for each of the data sets. Again, the addition of another variable improves the R2 of the models for each data set,




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with the combined data set improving the most (0.0539 to R2 = 0.3674), while others barely improve at all over the two-variable models (UF Trips 1-6 up only 0.0017 to R2 = Table 3.4: F values and p values for the best two-variable regression models. Data Set Variable F Value p Value
All Sets TSS 415.32 < 0.0001
Color 230.79 < 0.0001
HBOI Year 1 TSS 69.97 < 0.0001
Color 53.98 < 0.0001
HBOI Year 2 Color 42.31 < 0.0001
Chla 37.66 < 0.0001
UF Trips 1-6 TSS 113.22 < 0.0001
Chla 16.93 < 0.0001
UF Trips 7-12 Color 23.68 < 0.0001
Chla 29.36 < 0.0001
WQMN 1996-1998 TSS 89.55 < 0.0001
Color 69.47 < 0.0001
WQMN 1999 TSS 3.02 0.0938
Chla 1.47 0.2357
Phlips TSS 2.29 0.1499
Color 0.85 0.3715
SERC Color 132.64 < 0.0001
Chla 10.49 0.0021

0.4411) (Table 3.6). With three variables, the models for the combined data set, HBOI Year 1, UF Trips 1-6, WQMN 1996-1998, and SERC all have R2 values indicating real world significance with SERC again having the highest R2 value with R2 = 0.7618.
Since the third variable is prescribed and not chosen from a pool of variables to give the best fit for the model, the third variable in many of the data sets ends up being




statistically insignificant at the 0.05 level. This, as shown in Table 3.7, is the case for both UF data sets. All three of the variables for WQMN 1999 and Phlips showed no statistical significance at the 0.05 level.

Table 3.5: Best three-variable regression model for each data set. Data Coefficient for Coefficient for Coefficient for Intercept
Set TSS Color Chl_a
All Sets 0.03275 0.01774 0.02373 0.18468
HBOI Year 1 0.07300 0.03110 0.00639 -0.57740
HBOI Year 2 0.02774 0.02176 0.02656 0.18644
UF Trips 1-6 0.05400 -0.00831 0.04914 0.45681
UF Trips 7-12 0.01064 0.01268 0.03810 0.26555
WQMN 1996-1998 0.02544 0.01458 0.00932 0.33958
WQMN 1999 0.02163 0.00281 0.04136 0.45431
Phlips 0.04421 0.03498 -0.00463 0.29913
SERC 0.01675 0.01632 0.01377 0.57898

Table 3.6: R2 values for the best three-variable model for each data set and the improvement in R2 over the two- variable model. Data Set R2 Improvement
All Sets 0.3674 0.0539
HBOI Year 1 0.3851 0.0029
HBOI Year 2 0.2849 0.0390
UF Trips 1-6 0.4411 0.0017
UF Trips 7-12 0.2904 0.0151
WQMN 1996-1998 0.3703 0.0111
WQMN 1999 0.1160 0.0016
Phlips 0.1310 0.0013
SERC 0.7618 0.0243